diff --git a/cirq/circuits/circuit.py b/cirq/circuits/circuit.py
index 7a7e85498eb..8a1e74f3a15 100644
--- a/cirq/circuits/circuit.py
+++ b/cirq/circuits/circuit.py
@@ -1035,7 +1035,7 @@ def _superoperator_(self) -> np.ndarray:
         if n > 10:
             raise ValueError(f"{n} > 10 qubits is too many to compute superoperator")
 
-        circuit_superoperator = np.eye(4 ** n)
+        circuit_superoperator = np.eye(4**n)
         for moment in self:
             full_moment = moment.expand_to(all_qubits)
             moment_superoperator = full_moment._superoperator_()
diff --git a/cirq/circuits/circuit_operation.py b/cirq/circuits/circuit_operation.py
index 89b260318e7..e05cc5fb7e0 100644
--- a/cirq/circuits/circuit_operation.py
+++ b/cirq/circuits/circuit_operation.py
@@ -300,7 +300,7 @@ def _mapped_single_loop(self, repetition_id: Optional[str] = None) -> 'cirq.Circ
             if self.qubit_map:
                 circuit = circuit.transform_qubits(lambda q: self.qubit_map.get(q, q))
             if isinstance(self.repetitions, INT_CLASSES) and self.repetitions < 0:
-                circuit = circuit ** -1
+                circuit = circuit**-1
             if self.measurement_key_map:
                 circuit = protocols.with_measurement_key_mapping(circuit, self.measurement_key_map)
             if self.param_resolver:
diff --git a/cirq/circuits/circuit_operation_test.py b/cirq/circuits/circuit_operation_test.py
index a92c7abbd1b..7b1cd884afd 100644
--- a/cirq/circuits/circuit_operation_test.py
+++ b/cirq/circuits/circuit_operation_test.py
@@ -307,12 +307,12 @@ def test_repeat(add_measurements, use_default_ids_for_initial_rep):
     if use_default_ids_for_initial_rep:
         op_with_reps = op_base.repeat(initial_repetitions)
         rep_ids = ['0', '1', '2']
-        assert op_base ** initial_repetitions == op_with_reps
+        assert op_base**initial_repetitions == op_with_reps
     else:
         rep_ids = ['a', 'b', 'c']
         op_with_reps = op_base.repeat(initial_repetitions, rep_ids)
-        assert op_base ** initial_repetitions != op_with_reps
-        assert (op_base ** initial_repetitions).replace(repetition_ids=rep_ids) == op_with_reps
+        assert op_base**initial_repetitions != op_with_reps
+        assert (op_base**initial_repetitions).replace(repetition_ids=rep_ids) == op_with_reps
     assert op_with_reps.repetitions == initial_repetitions
     assert op_with_reps.repetition_ids == rep_ids
     assert op_with_reps.repeat(1) is op_with_reps
@@ -322,7 +322,7 @@ def test_repeat(add_measurements, use_default_ids_for_initial_rep):
     op_with_consecutive_reps = op_with_reps.repeat(2)
     assert op_with_consecutive_reps.repetitions == final_repetitions
     assert op_with_consecutive_reps.repetition_ids == _full_join_string_lists(['0', '1'], rep_ids)
-    assert op_base ** final_repetitions != op_with_consecutive_reps
+    assert op_base**final_repetitions != op_with_consecutive_reps
 
     op_with_consecutive_reps = op_with_reps.repeat(2, ['a', 'b'])
     assert op_with_reps.repeat(repetition_ids=['a', 'b']) == op_with_consecutive_reps
@@ -357,7 +357,7 @@ def test_repeat_zero_times(add_measurements, use_repetition_ids, initial_reps):
     )
     result = cirq.Simulator().simulate(cirq.Circuit(op))
     assert np.allclose(result.state_vector(), [0, 1] if initial_reps % 2 else [1, 0])
-    result = cirq.Simulator().simulate(cirq.Circuit(op ** 0))
+    result = cirq.Simulator().simulate(cirq.Circuit(op**0))
     assert np.allclose(result.state_vector(), [1, 0])
 
 
@@ -378,7 +378,7 @@ def test_parameterized_repeat():
         cirq.Simulator().simulate(cirq.Circuit(op), param_resolver={'a': 1.5})
     with pytest.raises(ValueError, match='Circuit contains ops whose symbols were not specified'):
         cirq.Simulator().simulate(cirq.Circuit(op))
-    op = op ** -1
+    op = op**-1
     assert cirq.parameter_names(op) == {'a'}
     assert not cirq.has_unitary(op)
     result = cirq.Simulator().simulate(cirq.Circuit(op), param_resolver={'a': 0})
@@ -406,7 +406,7 @@ def test_parameterized_repeat():
         cirq.Simulator().simulate(cirq.Circuit(op), param_resolver={'a': 1.5, 'b': 1})
     with pytest.raises(ValueError, match='Circuit contains ops whose symbols were not specified'):
         cirq.Simulator().simulate(cirq.Circuit(op))
-    op = op ** 2.0
+    op = op**2.0
     assert cirq.parameter_names(op) == {'a', 'b'}
     assert not cirq.has_unitary(op)
     result = cirq.Simulator().simulate(cirq.Circuit(op), param_resolver={'a': 1, 'b': 1})
diff --git a/cirq/circuits/circuit_test.py b/cirq/circuits/circuit_test.py
index 05bacd7efd4..5cfb226f645 100644
--- a/cirq/circuits/circuit_test.py
+++ b/cirq/circuits/circuit_test.py
@@ -1307,7 +1307,7 @@ def test_next_moment_operating_on_distance(circuit_cls):
     assert c.next_moment_operating_on([a], 1, max_distance=500) == 4
 
     # Huge max distances should be handled quickly due to capping.
-    assert c.next_moment_operating_on([a], 5, max_distance=10 ** 100) is None
+    assert c.next_moment_operating_on([a], 5, max_distance=10**100) is None
 
     with pytest.raises(ValueError, match='Negative max_distance'):
         c.next_moment_operating_on([a], 0, max_distance=-1)
@@ -1396,7 +1396,7 @@ def test_prev_moment_operating_on_distance(circuit_cls):
     assert c.prev_moment_operating_on([a], 13, max_distance=500) == 1
 
     # Huge max distances should be handled quickly due to capping.
-    assert c.prev_moment_operating_on([a], 1, max_distance=10 ** 100) is None
+    assert c.prev_moment_operating_on([a], 1, max_distance=10**100) is None
 
     with pytest.raises(ValueError, match='Negative max_distance'):
         c.prev_moment_operating_on([a], 6, max_distance=-1)
@@ -1703,7 +1703,7 @@ def test_findall_operations_until_blocked(circuit_cls):
     )
 
 
-@pytest.mark.parametrize('seed', [randint(0, 2 ** 31)])
+@pytest.mark.parametrize('seed', [randint(0, 2**31)])
 @pytest.mark.parametrize('circuit_cls', [cirq.Circuit, cirq.FrozenCircuit])
 def test_findall_operations_until_blocked_docstring_examples(seed, circuit_cls):
     prng = np.random.RandomState(seed)
@@ -2861,7 +2861,7 @@ def pauli_error_probability(r: float, n_qubits: int) -> float:
         makes it simple to compute the serial composition of depolarizing channels. It
         is multiplicative under channel composition.
         """
-        d2 = 4 ** n_qubits
+        d2 = 4**n_qubits
         return (1 - r) * (d2 - 1) / d2
 
     def depolarize(r: float, n_qubits: int) -> cirq.DepolarizingChannel:
@@ -4062,9 +4062,9 @@ def test_submoments(circuit_cls):
         cirq.H.on(d),
         cirq.CZ.on(a, d),
         cirq.CZ.on(b, c),
-        (cirq.CNOT ** 0.5).on(a, d),
-        (cirq.CNOT ** 0.5).on(b, e),
-        (cirq.CNOT ** 0.5).on(c, f),
+        (cirq.CNOT**0.5).on(a, d),
+        (cirq.CNOT**0.5).on(b, e),
+        (cirq.CNOT**0.5).on(c, f),
         cirq.H.on(c),
         cirq.H.on(e),
     )
@@ -4191,15 +4191,12 @@ def test_measurement_key_mapping(circuit_cls):
     assert simulator.run(c).measurements == {'m1': 1, 'm2': 0}
     assert simulator.run(c_swapped).measurements == {'m1': 0, 'm2': 1}
 
-    assert (
-        cirq.with_measurement_key_mapping(
-            c,
-            {
-                'x': 'z',
-            },
-        ).all_measurement_key_names()
-        == {'m1', 'm2'}
-    )
+    assert cirq.with_measurement_key_mapping(
+        c,
+        {
+            'x': 'z',
+        },
+    ).all_measurement_key_names() == {'m1', 'm2'}
 
 
 @pytest.mark.parametrize('circuit_cls', [cirq.Circuit, cirq.FrozenCircuit])
@@ -4222,7 +4219,7 @@ def test_measurement_key_mapping_preserves_moments(circuit_cls):
 @pytest.mark.parametrize('circuit_cls', [cirq.Circuit, cirq.FrozenCircuit])
 def test_inverse(circuit_cls):
     a, b = cirq.LineQubit.range(2)
-    forward = circuit_cls((cirq.X ** 0.5)(a), (cirq.Y ** -0.2)(b), cirq.CZ(a, b))
+    forward = circuit_cls((cirq.X**0.5)(a), (cirq.Y**-0.2)(b), cirq.CZ(a, b))
     backward = circuit_cls((cirq.CZ ** (-1.0))(a, b), (cirq.X ** (-0.5))(a), (cirq.Y ** (0.2))(b))
     cirq.testing.assert_same_circuits(cirq.inverse(forward), backward)
 
@@ -4233,7 +4230,7 @@ def test_inverse(circuit_cls):
         cirq.inverse(no_inverse)
 
     # Default when there is no inverse for an op.
-    default = circuit_cls((cirq.X ** 0.5)(a), (cirq.Y ** -0.2)(b))
+    default = circuit_cls((cirq.X**0.5)(a), (cirq.Y**-0.2)(b))
     cirq.testing.assert_same_circuits(cirq.inverse(no_inverse, default), default)
     assert cirq.inverse(no_inverse, None) is None
 
@@ -4241,7 +4238,7 @@ def test_inverse(circuit_cls):
 @pytest.mark.parametrize('circuit_cls', [cirq.Circuit, cirq.FrozenCircuit])
 def test_pow_valid_only_for_minus_1(circuit_cls):
     a, b = cirq.LineQubit.range(2)
-    forward = circuit_cls((cirq.X ** 0.5)(a), (cirq.Y ** -0.2)(b), cirq.CZ(a, b))
+    forward = circuit_cls((cirq.X**0.5)(a), (cirq.Y**-0.2)(b), cirq.CZ(a, b))
 
     backward = circuit_cls((cirq.CZ ** (-1.0))(a, b), (cirq.X ** (-0.5))(a), (cirq.Y ** (0.2))(b))
     cirq.testing.assert_same_circuits(cirq.pow(forward, -1), backward)
@@ -4642,28 +4639,22 @@ def _measurement_key_name_(self):
     assert circuit_cls().all_measurement_key_names() == set()
 
     # Order does not matter.
-    assert (
-        circuit_cls(
-            cirq.Moment(
-                [
-                    cirq.measure(a, key='x'),
-                    cirq.measure(b, key='y'),
-                ]
-            )
-        ).all_measurement_key_names()
-        == {'x', 'y'}
-    )
-    assert (
-        circuit_cls(
-            cirq.Moment(
-                [
-                    cirq.measure(b, key='y'),
-                    cirq.measure(a, key='x'),
-                ]
-            )
-        ).all_measurement_key_names()
-        == {'x', 'y'}
-    )
+    assert circuit_cls(
+        cirq.Moment(
+            [
+                cirq.measure(a, key='x'),
+                cirq.measure(b, key='y'),
+            ]
+        )
+    ).all_measurement_key_names() == {'x', 'y'}
+    assert circuit_cls(
+        cirq.Moment(
+            [
+                cirq.measure(b, key='y'),
+                cirq.measure(a, key='x'),
+            ]
+        )
+    ).all_measurement_key_names() == {'x', 'y'}
 
 
 def test_zip():
diff --git a/cirq/circuits/moment.py b/cirq/circuits/moment.py
index 57f16e8e209..2b2a6e3a149 100644
--- a/cirq/circuits/moment.py
+++ b/cirq/circuits/moment.py
@@ -414,7 +414,7 @@ def kraus_tensors(op: 'cirq.Operation') -> Sequence[np.ndarray]:
         transpose = input_subscripts + '->' + output_subscripts
 
         r = []
-        d = 2 ** n
+        d = 2**n
         kss = [kraus_tensors(op) for op in self.operations]
         for ks in itertools.product(*kss):
             k = np.einsum(transpose, *ks)
diff --git a/cirq/circuits/moment_test.py b/cirq/circuits/moment_test.py
index c147ac771b5..dfdaefd0e53 100644
--- a/cirq/circuits/moment_test.py
+++ b/cirq/circuits/moment_test.py
@@ -409,10 +409,10 @@ def test_json_dict():
 def test_inverse():
     a, b, c = cirq.LineQubit.range(3)
     m = cirq.Moment([cirq.S(a), cirq.CNOT(b, c)])
-    assert m ** 1 is m
-    assert m ** -1 == cirq.Moment([cirq.S(a) ** -1, cirq.CNOT(b, c)])
-    assert m ** 0.5 == cirq.Moment([cirq.T(a), cirq.CNOT(b, c) ** 0.5])
-    assert cirq.inverse(m) == m ** -1
+    assert m**1 is m
+    assert m**-1 == cirq.Moment([cirq.S(a) ** -1, cirq.CNOT(b, c)])
+    assert m**0.5 == cirq.Moment([cirq.T(a), cirq.CNOT(b, c) ** 0.5])
+    assert cirq.inverse(m) == m**-1
     assert cirq.inverse(cirq.inverse(m)) == m
     assert cirq.inverse(cirq.Moment([cirq.measure(a)]), default=None) is None
 
diff --git a/cirq/circuits/optimization_pass_test.py b/cirq/circuits/optimization_pass_test.py
index 15184a0f149..a2fe27b489a 100644
--- a/cirq/circuits/optimization_pass_test.py
+++ b/cirq/circuits/optimization_pass_test.py
@@ -135,7 +135,7 @@ def test_point_optimizer_post_clean_up():
 
     def clean_up(operations):
         for op in operations:
-            yield op ** 0.5
+            yield op**0.5
 
     ReplaceWithXGates(post_clean_up=clean_up)(c)
 
diff --git a/cirq/contrib/acquaintance/executor_test.py b/cirq/contrib/acquaintance/executor_test.py
index 20e2d3572de..231e7ab9d5c 100644
--- a/cirq/contrib/acquaintance/executor_test.py
+++ b/cirq/contrib/acquaintance/executor_test.py
@@ -89,7 +89,7 @@ def random_diagonal_gates(
 ) -> Dict[Tuple[cirq.Qid, ...], cirq.Gate]:
 
     return {
-        Q: cirq.DiagonalGate(np.random.random(2 ** acquaintance_size))
+        Q: cirq.DiagonalGate(np.random.random(2**acquaintance_size))
         for Q in combinations(cirq.LineQubit.range(num_qubits), acquaintance_size)
     }
 
diff --git a/cirq/contrib/acquaintance/permutation_test.py b/cirq/contrib/acquaintance/permutation_test.py
index 2b347961265..a626d777326 100644
--- a/cirq/contrib/acquaintance/permutation_test.py
+++ b/cirq/contrib/acquaintance/permutation_test.py
@@ -184,7 +184,7 @@ def test_linear_permutation_gate_pow_not_implemented():
 def test_linear_permutation_gate_pow_identity(num_qubits, permutation):
     permutation_gate = cca.LinearPermutationGate(num_qubits, permutation)
 
-    assert permutation_gate ** 1 == permutation_gate
+    assert permutation_gate**1 == permutation_gate
 
 
 @pytest.mark.parametrize(
@@ -201,7 +201,7 @@ def test_linear_permutation_gate_pow_inverse(num_qubits, permutation, inverse):
     permutation_gate = cca.LinearPermutationGate(num_qubits, permutation)
     inverse_gate = cca.LinearPermutationGate(num_qubits, inverse)
 
-    assert permutation_gate ** -1 == inverse_gate
+    assert permutation_gate**-1 == inverse_gate
     assert cirq.inverse(permutation_gate) == inverse_gate
 
 
diff --git a/cirq/contrib/qasm_import/_parser.py b/cirq/contrib/qasm_import/_parser.py
index 35c5634b951..a3a56b8cf69 100644
--- a/cirq/contrib/qasm_import/_parser.py
+++ b/cirq/contrib/qasm_import/_parser.py
@@ -240,8 +240,8 @@ def __init__(self):
             qasm_gate='cswap', num_params=0, num_args=3, cirq_gate=ops.CSWAP
         ),
         'ccx': QasmGateStatement(qasm_gate='ccx', num_params=0, num_args=3, cirq_gate=ops.CCX),
-        'sdg': QasmGateStatement(qasm_gate='sdg', num_params=0, num_args=1, cirq_gate=ops.S ** -1),
-        'tdg': QasmGateStatement(qasm_gate='tdg', num_params=0, num_args=1, cirq_gate=ops.T ** -1),
+        'sdg': QasmGateStatement(qasm_gate='sdg', num_params=0, num_args=1, cirq_gate=ops.S**-1),
+        'tdg': QasmGateStatement(qasm_gate='tdg', num_params=0, num_args=1, cirq_gate=ops.T**-1),
     }
 
     all_gates = {**basic_gates, **qelib_gates}
diff --git a/cirq/contrib/qasm_import/_parser_test.py b/cirq/contrib/qasm_import/_parser_test.py
index 1cc82753980..d6113a8ee12 100644
--- a/cirq/contrib/qasm_import/_parser_test.py
+++ b/cirq/contrib/qasm_import/_parser_test.py
@@ -434,8 +434,8 @@ def test_unknown_function():
     ('h', cirq.H),
     ('s', cirq.S),
     ('t', cirq.T),
-    ('sdg', cirq.S ** -1),
-    ('tdg', cirq.T ** -1),
+    ('sdg', cirq.S**-1),
+    ('tdg', cirq.T**-1),
     ('sx', cirq.XPowGate(exponent=0.5)),
 ]
 
diff --git a/cirq/contrib/quantum_volume/quantum_volume.py b/cirq/contrib/quantum_volume/quantum_volume.py
index 902df622e83..042a895d4d4 100644
--- a/cirq/contrib/quantum_volume/quantum_volume.py
+++ b/cirq/contrib/quantum_volume/quantum_volume.py
@@ -86,7 +86,7 @@ def compute_heavy_set(circuit: cirq.Circuit) -> List[int]:
     # The output wave function is a vector from the result value (big-endian) to
     # the probability of that bit-string. Return all of the bit-string
     # values that have a probability greater than the median.
-    return [idx for idx, amp in enumerate(results.state_vector()) if np.abs(amp ** 2) > median]
+    return [idx for idx, amp in enumerate(results.state_vector()) if np.abs(amp**2) > median]
 
 
 @dataclass
diff --git a/cirq/contrib/quirk/quirk_gate.py b/cirq/contrib/quirk/quirk_gate.py
index eeef0daa379..32869194e1b 100644
--- a/cirq/contrib/quirk/quirk_gate.py
+++ b/cirq/contrib/quirk/quirk_gate.py
@@ -176,11 +176,11 @@ def z_to_quirk_op(gate: ops.ZPowGate) -> QuirkOp:
 
 
 def cz_to_quirk_op(gate: ops.CZPowGate) -> Optional[QuirkOp]:
-    return z_to_quirk_op(ops.Z ** gate.exponent).controlled()
+    return z_to_quirk_op(ops.Z**gate.exponent).controlled()
 
 
 def cnot_to_quirk_op(gate: ops.CXPowGate) -> Optional[QuirkOp]:
-    return x_to_quirk_op(ops.X ** gate.exponent).controlled()
+    return x_to_quirk_op(ops.X**gate.exponent).controlled()
 
 
 def h_to_quirk_op(gate: ops.HPowGate) -> Optional[QuirkOp]:
diff --git a/cirq/contrib/routing/initialization_test.py b/cirq/contrib/routing/initialization_test.py
index d92b2b2607f..66c2aea5b73 100644
--- a/cirq/contrib/routing/initialization_test.py
+++ b/cirq/contrib/routing/initialization_test.py
@@ -29,7 +29,7 @@ def get_seeded_initial_mapping(graph_seed, init_seed):
     return ccr.initialization.get_initial_mapping(logical_graph, device_graph, init_seed)
 
 
-@pytest.mark.parametrize('seed', [random.randint(0, 2 ** 32) for _ in range(10)])
+@pytest.mark.parametrize('seed', [random.randint(0, 2**32) for _ in range(10)])
 def test_initialization_reproducible_with_seed(seed):
     wrappers = (lambda s: s, np.random.RandomState)
     mappings = [
@@ -39,7 +39,7 @@ def test_initialization_reproducible_with_seed(seed):
     eq.add_equality_group(*mappings)
 
 
-@pytest.mark.parametrize('graph_seed,state', [(random.randint(0, 2 ** 32), np.random.get_state())])
+@pytest.mark.parametrize('graph_seed,state', [(random.randint(0, 2**32), np.random.get_state())])
 def test_initialization_with_no_seed(graph_seed, state):
     mappings = []
     for _ in range(3):
diff --git a/cirq/contrib/routing/router_test.py b/cirq/contrib/routing/router_test.py
index 72564355226..7d82eb6a92d 100644
--- a/cirq/contrib/routing/router_test.py
+++ b/cirq/contrib/routing/router_test.py
@@ -24,7 +24,7 @@
 
 
 def random_seed():
-    return random.randint(0, 2 ** 32)
+    return random.randint(0, 2**32)
 
 
 @pytest.mark.parametrize(
diff --git a/cirq/devices/noise_model_test.py b/cirq/devices/noise_model_test.py
index 247961b0c33..ad4c5809f08 100644
--- a/cirq/devices/noise_model_test.py
+++ b/cirq/devices/noise_model_test.py
@@ -121,7 +121,7 @@ def test_constant_qubit_noise():
     cirq.testing.assert_equivalent_repr(damp_all)
 
     with pytest.raises(ValueError, match='num_qubits'):
-        _ = cirq.ConstantQubitNoiseModel(cirq.CNOT ** 0.01)
+        _ = cirq.ConstantQubitNoiseModel(cirq.CNOT**0.01)
 
 
 def test_noise_composition():
@@ -129,7 +129,7 @@ def test_noise_composition():
     # long as the noise operators commute with one another.
     a, b, c = cirq.LineQubit.range(3)
     noise_z = cirq.ConstantQubitNoiseModel(cirq.Z)
-    noise_inv_s = cirq.ConstantQubitNoiseModel(cirq.S ** -1)
+    noise_inv_s = cirq.ConstantQubitNoiseModel(cirq.S**-1)
     base_moments = [cirq.Moment([cirq.X(a)]), cirq.Moment([cirq.Y(b)]), cirq.Moment([cirq.H(c)])]
     circuit_z = cirq.Circuit(noise_z.noisy_moments(base_moments, [a, b, c]))
     circuit_s = cirq.Circuit(noise_inv_s.noisy_moments(base_moments, [a, b, c]))
@@ -154,7 +154,7 @@ def test_noise_composition():
 
 
 def test_constant_qubit_noise_repr():
-    cirq.testing.assert_equivalent_repr(cirq.ConstantQubitNoiseModel(cirq.X ** 0.01))
+    cirq.testing.assert_equivalent_repr(cirq.ConstantQubitNoiseModel(cirq.X**0.01))
 
 
 def test_wrap():
@@ -168,8 +168,8 @@ def noisy_operation(self, operation):
     assert cirq.NoiseModel.from_noise_model_like(
         cirq.depolarize(0.1)
     ) == cirq.ConstantQubitNoiseModel(cirq.depolarize(0.1))
-    assert cirq.NoiseModel.from_noise_model_like(cirq.Z ** 0.01) == cirq.ConstantQubitNoiseModel(
-        cirq.Z ** 0.01
+    assert cirq.NoiseModel.from_noise_model_like(cirq.Z**0.01) == cirq.ConstantQubitNoiseModel(
+        cirq.Z**0.01
     )
     assert cirq.NoiseModel.from_noise_model_like(forget) is forget
 
@@ -177,7 +177,7 @@ def noisy_operation(self, operation):
         _ = cirq.NoiseModel.from_noise_model_like('test')
 
     with pytest.raises(ValueError, match='Multi-qubit gate'):
-        _ = cirq.NoiseModel.from_noise_model_like(cirq.CZ ** 0.01)
+        _ = cirq.NoiseModel.from_noise_model_like(cirq.CZ**0.01)
 
 
 def test_gate_substitution_noise_model():
diff --git a/cirq/devices/noise_utils.py b/cirq/devices/noise_utils.py
index 22e21aab89d..3a38ee40abd 100644
--- a/cirq/devices/noise_utils.py
+++ b/cirq/devices/noise_utils.py
@@ -109,7 +109,7 @@ def decay_constant_to_xeb_fidelity(decay_constant: float, num_qubits: int = 2) -
     Returns:
         Calculated XEB fidelity.
     """
-    N = 2 ** num_qubits
+    N = 2**num_qubits
     return 1 - ((1 - decay_constant) * (1 - 1 / N))
 
 
@@ -123,7 +123,7 @@ def decay_constant_to_pauli_error(decay_constant: float, num_qubits: int = 1) ->
     Returns:
         Calculated Pauli error.
     """
-    N = 2 ** num_qubits
+    N = 2**num_qubits
     return (1 - decay_constant) * (1 - 1 / N / N)
 
 
@@ -137,7 +137,7 @@ def pauli_error_to_decay_constant(pauli_error: float, num_qubits: int = 1) -> fl
     Returns:
         Calculated depolarization decay constant.
     """
-    N = 2 ** num_qubits
+    N = 2**num_qubits
     return 1 - (pauli_error / (1 - 1 / N / N))
 
 
@@ -151,7 +151,7 @@ def xeb_fidelity_to_decay_constant(xeb_fidelity: float, num_qubits: int = 2) ->
     Returns:
         Calculated depolarization decay constant.
     """
-    N = 2 ** num_qubits
+    N = 2**num_qubits
     return 1 - (1 - xeb_fidelity) / (1 - 1 / N)
 
 
@@ -181,7 +181,7 @@ def average_error(decay_constant: float, num_qubits: int = 1) -> float:
     Returns:
         Calculated average error.
     """
-    N = 2 ** num_qubits
+    N = 2**num_qubits
     return (1 - decay_constant) * (1 - 1 / N)
 
 
diff --git a/cirq/devices/thermal_noise_model_test.py b/cirq/devices/thermal_noise_model_test.py
index 182fba026fe..42f5375934a 100644
--- a/cirq/devices/thermal_noise_model_test.py
+++ b/cirq/devices/thermal_noise_model_test.py
@@ -277,7 +277,7 @@ def test_noisy_moment_two_qubit():
         dephase_rate_GHz={q0: 3e-4, q1: 4e-4},
         require_physical_tag=False,
     )
-    gate = cirq.CZ ** 0.5
+    gate = cirq.CZ**0.5
     moment = cirq.Moment(gate.on(q0, q1))
     noisy_moment = model.noisy_moment(moment, system_qubits=[q0, q1])
     assert noisy_moment[0] == moment
diff --git a/cirq/experiments/cross_entropy_benchmarking.py b/cirq/experiments/cross_entropy_benchmarking.py
index 3d3dfd1571a..b14e428271d 100644
--- a/cirq/experiments/cross_entropy_benchmarking.py
+++ b/cirq/experiments/cross_entropy_benchmarking.py
@@ -95,7 +95,7 @@ class SpecklePurityDepolarizingModel(CrossEntropyDepolarizingModel):
     @property
     def purity(self) -> float:
         """The purity. Equal to p**2, where p is the cycle depolarization."""
-        return self.cycle_depolarization ** 2
+        return self.cycle_depolarization**2
 
 
 @protocols.json_serializable_dataclass(frozen=True)
@@ -235,7 +235,7 @@ def _fit_exponential_decay(x: Sequence[int], y: Sequence[float]) -> Tuple[np.nda
 
     # Perform nonlinear least squares
     def f(a, S, p):
-        return S * p ** a
+        return S * p**a
 
     return optimize.curve_fit(f, x, y, p0=p0)
 
@@ -382,8 +382,8 @@ def cross_entropy_benchmarking(
     # all trials in two dictionaries. The keys of the dictionaries are the
     # numbers of cycles. The values are 2D arrays with each row being the
     # probabilities obtained from a single trial.
-    probs_meas = {n: np.zeros((num_circuits, 2 ** num_qubits)) for n in cycle_range}
-    probs_th = {n: np.zeros((num_circuits, 2 ** num_qubits)) for n in cycle_range}
+    probs_meas = {n: np.zeros((num_circuits, 2**num_qubits)) for n in cycle_range}
+    probs_th = {n: np.zeros((num_circuits, 2**num_qubits)) for n in cycle_range}
 
     for k in range(num_circuits):
 
@@ -552,14 +552,14 @@ def _compute_fidelity(probs_th: np.ndarray, probs_meas: np.ndarray) -> float:
     """
     _, num_states = probs_th.shape
     pp_cross = probs_th * probs_meas
-    pp_th = probs_th ** 2
+    pp_th = probs_th**2
     f_meas = np.mean(num_states * np.sum(pp_cross, axis=1) - 1.0)
     f_th = np.mean(num_states * np.sum(pp_th, axis=1) - 1.0)
     return float(f_meas / f_th)
 
 
 def _random_half_rotations(qubits: Sequence[ops.Qid], num_layers: int) -> List[List[ops.OP_TREE]]:
-    rot_ops = [ops.X ** 0.5, ops.Y ** 0.5, ops.PhasedXPowGate(phase_exponent=0.25, exponent=0.5)]
+    rot_ops = [ops.X**0.5, ops.Y**0.5, ops.PhasedXPowGate(phase_exponent=0.25, exponent=0.5)]
     num_qubits = len(qubits)
     rand_nums = np.random.choice(3, (num_qubits, num_layers))
     single_q_layers: List[List[ops.OP_TREE]] = []
diff --git a/cirq/experiments/cross_entropy_benchmarking_test.py b/cirq/experiments/cross_entropy_benchmarking_test.py
index 0688a7877ba..f4b0fcc9336 100644
--- a/cirq/experiments/cross_entropy_benchmarking_test.py
+++ b/cirq/experiments/cross_entropy_benchmarking_test.py
@@ -36,18 +36,18 @@ def test_cross_entropy_benchmarking():
 
     # Sanity check single-qubit-gate causes error
     with pytest.raises(ValueError):
-        build_entangling_layers(qubits, cirq.Z ** 0.91)
+        build_entangling_layers(qubits, cirq.Z**0.91)
 
     # Build a sequence of CZ gates.
-    interleaved_ops = build_entangling_layers(qubits, cirq.CZ ** 0.91)
+    interleaved_ops = build_entangling_layers(qubits, cirq.CZ**0.91)
 
     # Specify a set of single-qubit rotations. Pick prime numbers for the
     # exponent to avoid evolving the system into a basis state.
     single_qubit_rots = [
-        [cirq.X ** 0.37],
-        [cirq.Y ** 0.73, cirq.X ** 0.53],
-        [cirq.Z ** 0.61, cirq.X ** 0.43],
-        [cirq.Y ** 0.19],
+        [cirq.X**0.37],
+        [cirq.Y**0.73, cirq.X**0.53],
+        [cirq.Z**0.61, cirq.X**0.43],
+        [cirq.Y**0.19],
     ]
 
     # Simulate XEB using the default single-qubit gate set without two-qubit
@@ -104,7 +104,7 @@ def test_cross_entropy_result_depolarizing_models():
     S = 0.8
     p = 0.99
     data = [
-        CrossEntropyPair(num_cycle=d, xeb_fidelity=S * p ** d + prng.normal(scale=0.01))
+        CrossEntropyPair(num_cycle=d, xeb_fidelity=S * p**d + prng.normal(scale=0.01))
         for d in range(10, 211, 20)
     ]
     purity_data = [
@@ -116,7 +116,7 @@ def test_cross_entropy_result_depolarizing_models():
     purity_model = result.purity_depolarizing_model()
     np.testing.assert_allclose(model.spam_depolarization, S, atol=1e-2)
     np.testing.assert_allclose(model.cycle_depolarization, p, atol=1e-2)
-    np.testing.assert_allclose(purity_model.purity, p ** 2, atol=1e-2)
+    np.testing.assert_allclose(purity_model.purity, p**2, atol=1e-2)
 
 
 def test_cross_entropy_result_repr():
diff --git a/cirq/experiments/fidelity_estimation_test.py b/cirq/experiments/fidelity_estimation_test.py
index ed6ba5b9c1a..3eaf428a7f3 100644
--- a/cirq/experiments/fidelity_estimation_test.py
+++ b/cirq/experiments/fidelity_estimation_test.py
@@ -36,7 +36,7 @@ def sample_noisy_bitstrings(
 
 
 def make_random_quantum_circuit(qubits: Sequence[cirq.Qid], depth: int) -> cirq.Circuit:
-    SQ_GATES = [cirq.X ** 0.5, cirq.Y ** 0.5, cirq.T]
+    SQ_GATES = [cirq.X**0.5, cirq.Y**0.5, cirq.T]
     circuit = cirq.Circuit()
     cz_start = 0
     for q in qubits:
@@ -152,7 +152,7 @@ def test_least_squares_xeb_fidelity_from_expectations():
     depolarization = 0.5
 
     n_qubits = 5
-    dim = 2 ** n_qubits
+    dim = 2**n_qubits
     n_circuits = 10
     qubits = cirq.LineQubit.range(n_qubits)
 
@@ -170,7 +170,7 @@ def test_least_squares_xeb_fidelity_from_expectations():
         probabilities = cirq.state_vector_to_probabilities(amplitudes)
 
         measured_expectations_lin.append(dim * np.mean(probabilities[bitstrings]))
-        exact_expectations_lin.append(dim * np.sum(probabilities ** 2))
+        exact_expectations_lin.append(dim * np.sum(probabilities**2))
 
         measured_expectations_log.append(np.mean(np.log(dim * probabilities[bitstrings])))
         exact_expectations_log.append(np.sum(probabilities * np.log(dim * probabilities)))
@@ -204,7 +204,7 @@ def test_least_squares_xeb_fidelity_from_probabilities():
     depolarization = 0.5
 
     n_qubits = 5
-    dim = 2 ** n_qubits
+    dim = 2**n_qubits
     n_circuits = 10
     qubits = cirq.LineQubit.range(n_qubits)
 
diff --git a/cirq/experiments/grid_parallel_two_qubit_xeb_test.py b/cirq/experiments/grid_parallel_two_qubit_xeb_test.py
index 92db8bf13f9..bfe71138b36 100644
--- a/cirq/experiments/grid_parallel_two_qubit_xeb_test.py
+++ b/cirq/experiments/grid_parallel_two_qubit_xeb_test.py
@@ -18,7 +18,7 @@ def test_estimate_parallel_two_qubit_xeb_fidelity_on_grid_no_noise(tmpdir):
     # No noise, fidelities should be close to 1
     base_dir = os.path.abspath(tmpdir)
     qubits = cirq.GridQubit.square(2)
-    two_qubit_gate = cirq.ISWAP ** 0.5
+    two_qubit_gate = cirq.ISWAP**0.5
     cycles = [5, 10, 15]
     data_collection_id = collect_grid_parallel_two_qubit_xeb_data(
         sampler=cirq.Simulator(seed=34310, split_untangled_states=False),
@@ -50,7 +50,7 @@ def test_estimate_parallel_two_qubit_xeb_fidelity_on_grid_depolarizing(tmpdir):
     # With depolarizing probability e
     base_dir = os.path.abspath(tmpdir)
     qubits = cirq.GridQubit.square(2)
-    two_qubit_gate = cirq.ISWAP ** 0.5
+    two_qubit_gate = cirq.ISWAP**0.5
     cycles = [5, 10, 15]
     e = 0.01
     data_collection_id = collect_grid_parallel_two_qubit_xeb_data(
@@ -85,7 +85,7 @@ def test_estimate_parallel_two_qubit_xeb_fidelity_on_grid_concurrent(tmpdir):
     # Use multiple threads during data collection
     base_dir = os.path.abspath(tmpdir)
     qubits = cirq.GridQubit.square(2)
-    two_qubit_gate = cirq.ISWAP ** 0.5
+    two_qubit_gate = cirq.ISWAP**0.5
     cycles = [5, 10, 15]
     data_collection_id = collect_grid_parallel_two_qubit_xeb_data(
         sampler=cirq.Simulator(seed=34310),
diff --git a/cirq/experiments/n_qubit_tomography.py b/cirq/experiments/n_qubit_tomography.py
index 87caffb94c4..be9b444a800 100644
--- a/cirq/experiments/n_qubit_tomography.py
+++ b/cirq/experiments/n_qubit_tomography.py
@@ -98,7 +98,7 @@ def _make_state_tomography_matrix(
             rotation sequence and bit string outcome for that rotation sequence.
         """
         num_rots = len(self.rot_sweep)
-        num_states = 2 ** self.num_qubits
+        num_states = 2**self.num_qubits
 
         # Unitary matrices of each rotation circuit.
         unitaries = np.array(
@@ -128,7 +128,7 @@ def fit_density_matrix(self, counts: np.ndarray) -> TomographyResult:
         probs = counts / np.sum(counts, axis=1)[:, np.newaxis]
         # use least squares to get solution.
         c, _, _, _ = np.linalg.lstsq(self.mat, np.asarray(probs).flat, rcond=-1)
-        rho = c.reshape((2 ** self.num_qubits, 2 ** self.num_qubits))
+        rho = c.reshape((2**self.num_qubits, 2**self.num_qubits))
         return TomographyResult(rho)
 
 
diff --git a/cirq/experiments/n_qubit_tomography_test.py b/cirq/experiments/n_qubit_tomography_test.py
index d6a2a4488bd..a873700401d 100644
--- a/cirq/experiments/n_qubit_tomography_test.py
+++ b/cirq/experiments/n_qubit_tomography_test.py
@@ -24,7 +24,7 @@
 def test_state_tomography_diagonal():
     n = 2
     qubits = cirq.LineQubit.range(n)
-    for state in range(2 ** n):
+    for state in range(2**n):
         circuit = cirq.Circuit()
         for i, q in enumerate(qubits):
             bit = state & (1 << (n - i - 1))
@@ -37,7 +37,7 @@ def test_state_tomography_diagonal():
             repetitions=1000,
             prerotations=[(0, 0), (0, 0.5), (0.5, 0.5)],
         )
-        should_be = np.zeros((2 ** n, 2 ** n))
+        should_be = np.zeros((2**n, 2**n))
         should_be[state, state] = 1
         assert np.allclose(res.data, should_be, atol=0.05)
 
diff --git a/cirq/experiments/purity_estimation.py b/cirq/experiments/purity_estimation.py
index 7bdf61e9b2d..3b581bdf551 100644
--- a/cirq/experiments/purity_estimation.py
+++ b/cirq/experiments/purity_estimation.py
@@ -58,5 +58,5 @@ def purity_from_probabilities(
         implementation of a quantum circuit.
     """
     D = hilbert_space_dimension
-    porter_thomas_variance = (D - 1) / (D + 1) / D ** 2
+    porter_thomas_variance = (D - 1) / (D + 1) / D**2
     return np.var(probabilities) / porter_thomas_variance
diff --git a/cirq/experiments/qubit_characterizations.py b/cirq/experiments/qubit_characterizations.py
index e37ebf40d11..0990dc64ecb 100644
--- a/cirq/experiments/qubit_characterizations.py
+++ b/cirq/experiments/qubit_characterizations.py
@@ -519,7 +519,7 @@ def _measurement(two_qubit_circuit: circuits.Circuit) -> np.ndarray:
     # different basis rotations).
     probs = np.array([])
 
-    rots = [ops.X ** 0, ops.X ** 0.5, ops.Y ** 0.5]
+    rots = [ops.X**0, ops.X**0.5, ops.Y**0.5]
 
     # Represents the coefficients in front of the c_ij's (-1, 0 or 1) in the
     # system of 27 linear equations.
@@ -778,14 +778,14 @@ def _single_qubit_cliffords() -> Cliffords:
     c1_in_xz: List[List['cirq.Gate']] = []
 
     for phi_0, phi_1 in itertools.product([1.0, 0.5, -0.5], [0.0, 0.5, -0.5]):
-        c1_in_xy.append([X ** phi_0, Y ** phi_1])
-        c1_in_xy.append([Y ** phi_0, X ** phi_1])
-        c1_in_xz.append([X ** phi_0, Z ** phi_1])
-        c1_in_xz.append([Z ** phi_0, X ** phi_1])
+        c1_in_xy.append([X**phi_0, Y**phi_1])
+        c1_in_xy.append([Y**phi_0, X**phi_1])
+        c1_in_xz.append([X**phi_0, Z**phi_1])
+        c1_in_xz.append([Z**phi_0, X**phi_1])
 
     # identity
-    c1_in_xy.append([X ** 0.0])
-    c1_in_xz.append([X ** 0.0])
+    c1_in_xy.append([X**0.0])
+    c1_in_xz.append([X**0.0])
 
     c1_in_xy.append([Y, X])
     c1_in_xz.append([Z, X])
@@ -797,7 +797,7 @@ def _single_qubit_cliffords() -> Cliffords:
         [-0.5, 0.5, -0.5],
     ]
     for y0, x, y1 in phi_xy:
-        c1_in_xy.append([Y ** y0, X ** x, Y ** y1])
+        c1_in_xy.append([Y**y0, X**x, Y**y1])
 
     phi_xz = [
         [0.5, 0.5, -0.5],
@@ -806,22 +806,22 @@ def _single_qubit_cliffords() -> Cliffords:
         [-0.5, 0.5, -0.5],
     ]
     for z0, x, z1 in phi_xz:
-        c1_in_xz.append([Z ** z0, X ** x, Z ** z1])
+        c1_in_xz.append([Z**z0, X**x, Z**z1])
 
     s1: List[List['cirq.Gate']] = [
-        [X ** 0.0],
-        [Y ** 0.5, X ** 0.5],
-        [X ** -0.5, Y ** -0.5],
+        [X**0.0],
+        [Y**0.5, X**0.5],
+        [X**-0.5, Y**-0.5],
     ]
     s1_x: List[List['cirq.Gate']] = [
-        [X ** 0.5],
-        [X ** 0.5, Y ** 0.5, X ** 0.5],
-        [Y ** -0.5],
+        [X**0.5],
+        [X**0.5, Y**0.5, X**0.5],
+        [Y**-0.5],
     ]
     s1_y: List[List['cirq.Gate']] = [
-        [Y ** 0.5],
-        [X ** -0.5, Y ** -0.5, X ** 0.5],
-        [Y, X ** 0.5],
+        [Y**0.5],
+        [X**-0.5, Y**-0.5, X**0.5],
+        [Y, X**0.5],
     ]
 
     return Cliffords(c1_in_xy, c1_in_xz, s1, s1_x, s1_y)
diff --git a/cirq/experiments/random_quantum_circuit_generation.py b/cirq/experiments/random_quantum_circuit_generation.py
index 1a57b7b6af8..04243631bf1 100644
--- a/cirq/experiments/random_quantum_circuit_generation.py
+++ b/cirq/experiments/random_quantum_circuit_generation.py
@@ -186,8 +186,8 @@ def random_rotations_between_two_qubit_circuit(
         ['cirq.Qid', 'cirq.Qid', 'np.random.RandomState'], 'cirq.OP_TREE'
     ] = lambda a, b, _: ops.CZPowGate()(a, b),
     single_qubit_gates: Sequence['cirq.Gate'] = (
-        ops.X ** 0.5,
-        ops.Y ** 0.5,
+        ops.X**0.5,
+        ops.Y**0.5,
         ops.PhasedXPowGate(phase_exponent=0.25, exponent=0.5),
     ),
     add_final_single_qubit_layer: bool = True,
@@ -520,7 +520,7 @@ def pair_gen():
 def get_grid_interaction_layer_circuit(
     device_graph: nx.Graph,
     pattern: Sequence[GridInteractionLayer] = HALF_GRID_STAGGERED_PATTERN,
-    two_qubit_gate=ops.ISWAP ** 0.5,
+    two_qubit_gate=ops.ISWAP**0.5,
 ) -> 'cirq.Circuit':
     """Create a circuit representation of a grid interaction pattern on a given device topology.
 
@@ -554,8 +554,8 @@ def random_rotations_between_grid_interaction_layers_circuit(
     ] = lambda a, b, _: ops.CZPowGate()(a, b),
     pattern: Sequence[GridInteractionLayer] = GRID_STAGGERED_PATTERN,
     single_qubit_gates: Sequence['cirq.Gate'] = (
-        ops.X ** 0.5,
-        ops.Y ** 0.5,
+        ops.X**0.5,
+        ops.Y**0.5,
         ops.PhasedXPowGate(phase_exponent=0.25, exponent=0.5),
     ),
     add_final_single_qubit_layer: bool = True,
diff --git a/cirq/experiments/random_quantum_circuit_generation_test.py b/cirq/experiments/random_quantum_circuit_generation_test.py
index cfa25fcec93..33527269503 100644
--- a/cirq/experiments/random_quantum_circuit_generation_test.py
+++ b/cirq/experiments/random_quantum_circuit_generation_test.py
@@ -92,7 +92,7 @@ def test_generate_library_of_2q_circuits():
 def test_generate_library_of_2q_circuits_custom_qubits():
     circuits = generate_library_of_2q_circuits(
         n_library_circuits=5,
-        two_qubit_gate=cirq.ISWAP ** 0.5,
+        two_qubit_gate=cirq.ISWAP**0.5,
         max_cycle_depth=13,
         q0=cirq.GridQubit(9, 9),
         q1=cirq.NamedQubit('hi mom'),
@@ -104,7 +104,7 @@ def test_generate_library_of_2q_circuits_custom_qubits():
         for m1, m2 in zip(circuit.moments[::2], circuit.moments[1::2]):
             assert len(m1.operations) == 2  # single qubit layer
             assert len(m2.operations) == 1
-            assert m2.operations[0].gate == cirq.ISWAP ** 0.5
+            assert m2.operations[0].gate == cirq.ISWAP**0.5
 
 
 def _gridqubits_to_graph_device(qubits: Iterable[cirq.GridQubit]):
@@ -208,7 +208,7 @@ def test_get_grid_interaction_layer_circuit():
     graph = _gridqubits_to_graph_device(cirq.GridQubit.rect(3, 3))
     layer_circuit = get_grid_interaction_layer_circuit(graph)
 
-    sqrtisw = cirq.ISWAP ** 0.5
+    sqrtisw = cirq.ISWAP**0.5
     gq = cirq.GridQubit
     should_be = cirq.Circuit(
         # Vertical
@@ -273,7 +273,7 @@ def __init__(self):
             20,
             lambda a, b, _: cirq.CZ(a, b),
             cirq.experiments.GRID_STAGGERED_PATTERN,
-            (cirq.X ** 0.5, cirq.Y ** 0.5, cirq.Z ** 0.5),
+            (cirq.X**0.5, cirq.Y**0.5, cirq.Z**0.5),
             True,
             1234,
             41,
@@ -285,7 +285,7 @@ def __init__(self):
             20,
             lambda a, b, _: FakeSycamoreGate()(a, b),
             cirq.experiments.HALF_GRID_STAGGERED_PATTERN,
-            (cirq.X ** 0.5, cirq.Y ** 0.5, cirq.Z ** 0.5),
+            (cirq.X**0.5, cirq.Y**0.5, cirq.Z**0.5),
             True,
             1234,
             41,
@@ -297,7 +297,7 @@ def __init__(self):
             21,
             lambda a, b, _: cirq.CZ(a, b),
             cirq.experiments.GRID_ALIGNED_PATTERN,
-            (cirq.X ** 0.5, cirq.Y ** 0.5, cirq.Z ** 0.5),
+            (cirq.X**0.5, cirq.Y**0.5, cirq.Z**0.5),
             True,
             1234,
             43,
@@ -309,7 +309,7 @@ def __init__(self):
             22,
             _cz_with_adjacent_z_rotations,
             cirq.experiments.GRID_STAGGERED_PATTERN,
-            (cirq.X ** 0.5, cirq.Y ** 0.5, cirq.Z ** 0.5),
+            (cirq.X**0.5, cirq.Y**0.5, cirq.Z**0.5),
             True,
             1234,
             89,
@@ -321,7 +321,7 @@ def __init__(self):
             23,
             lambda a, b, _: cirq.CZ(a, b),
             cirq.experiments.GRID_ALIGNED_PATTERN,
-            (cirq.X ** 0.5, cirq.Y ** 0.5, cirq.Z ** 0.5),
+            (cirq.X**0.5, cirq.Y**0.5, cirq.Z**0.5),
             False,
             1234,
             46,
@@ -333,7 +333,7 @@ def __init__(self):
             24,
             lambda a, b, _: cirq.CZ(a, b),
             cirq.experiments.GRID_ALIGNED_PATTERN,
-            (cirq.X ** 0.5, cirq.X ** 0.5),
+            (cirq.X**0.5, cirq.X**0.5),
             True,
             1234,
             49,
diff --git a/cirq/experiments/readout_confusion_matrix_test.py b/cirq/experiments/readout_confusion_matrix_test.py
index 5e74d6eeba6..228b6f90de3 100644
--- a/cirq/experiments/readout_confusion_matrix_test.py
+++ b/cirq/experiments/readout_confusion_matrix_test.py
@@ -20,9 +20,9 @@
 
 
 def get_expected_cm(num_qubits: int, p0: float, p1: float):
-    expected_cm = np.zeros((2 ** num_qubits,) * 2)
-    for i in range(2 ** num_qubits):
-        for j in range(2 ** num_qubits):
+    expected_cm = np.zeros((2**num_qubits,) * 2)
+    for i in range(2**num_qubits):
+        for j in range(2**num_qubits):
             p = 1.0
             for k in range(num_qubits):
                 b0 = (i >> k) & 1
diff --git a/cirq/experiments/t2_decay_experiment.py b/cirq/experiments/t2_decay_experiment.py
index 6c17f74e2aa..370515f1e72 100644
--- a/cirq/experiments/t2_decay_experiment.py
+++ b/cirq/experiments/t2_decay_experiment.py
@@ -423,7 +423,7 @@ def plot_bloch_vector(self, ax: Optional[plt.Axes] = None, **plot_kwargs: Any) -
 
         # Estimate length of Bloch vector (projected to xy plane)
         # by squaring <X> and <Y> expectation values
-        bloch_vector = self._expectation_pauli_x ** 2 + self._expectation_pauli_y ** 2
+        bloch_vector = self._expectation_pauli_x**2 + self._expectation_pauli_y**2
 
         ax.plot(self._expectation_pauli_x['delay_ns'], bloch_vector['value'], 'r+-', **plot_kwargs)
         ax.set_xlabel(r"Delay between initialization and measurement (nanoseconds)")
diff --git a/cirq/experiments/t2_decay_experiment_test.py b/cirq/experiments/t2_decay_experiment_test.py
index a626ae8e263..ede53b4f610 100644
--- a/cirq/experiments/t2_decay_experiment_test.py
+++ b/cirq/experiments/t2_decay_experiment_test.py
@@ -155,7 +155,7 @@ def noisy_moment(self, moment, system_qubits):
                 default=cirq.Duration(nanos=1),
             )
             phase = duration.total_nanos() / 100.0
-            yield (cirq.Y ** phase).on_each(system_qubits)
+            yield (cirq.Y**phase).on_each(system_qubits)
             yield moment
 
     pulses = [1] if experiment_type == t2.ExperimentType.CPMG else None
diff --git a/cirq/experiments/xeb_fitting.py b/cirq/experiments/xeb_fitting.py
index b277d55a7b3..3adc79488ab 100644
--- a/cirq/experiments/xeb_fitting.py
+++ b/cirq/experiments/xeb_fitting.py
@@ -100,7 +100,7 @@ def benchmark_2q_xeb_fidelities(
     D = 4  # two qubits
     pure_probs = np.array(df['pure_probs'].to_list())
     sampled_probs = np.array(df['sampled_probs'].to_list())
-    df['e_u'] = np.sum(pure_probs ** 2, axis=1)
+    df['e_u'] = np.sum(pure_probs**2, axis=1)
     df['u_u'] = np.sum(pure_probs, axis=1) / D
     df['m_u'] = np.sum(pure_probs * sampled_probs, axis=1)
     df['y'] = df['m_u'] - df['u_u']
@@ -539,7 +539,7 @@ def exponential_decay(cycle_depths: np.ndarray, a: float, layer_fid: float) -> n
         a: A scale parameter in the exponential function.
         layer_fid: The base of the exponent in the exponential function.
     """
-    return a * layer_fid ** cycle_depths
+    return a * layer_fid**cycle_depths
 
 
 def _fit_exponential_decay(
diff --git a/cirq/experiments/xeb_fitting_test.py b/cirq/experiments/xeb_fitting_test.py
index 9cb350195c2..ceabbd48f45 100644
--- a/cirq/experiments/xeb_fitting_test.py
+++ b/cirq/experiments/xeb_fitting_test.py
@@ -103,7 +103,7 @@ def _manhattan_distance(qubit1: cirq.GridQubit, qubit2: cirq.GridQubit) -> int:
 
 def test_benchmark_2q_xeb_fidelities_parallel():
     circuits = rqcg.generate_library_of_2q_circuits(
-        n_library_circuits=5, two_qubit_gate=cirq.ISWAP ** 0.5, max_cycle_depth=4
+        n_library_circuits=5, two_qubit_gate=cirq.ISWAP**0.5, max_cycle_depth=4
     )
     cycle_depths = [2, 3, 4]
     graph = _gridqubits_to_graph_device(cirq.GridQubit.rect(2, 2))
@@ -155,7 +155,7 @@ def _summary_stats(row):
     D = 4  # two qubits
     pure_probs = np.array(df['pure_probs'].to_list())
     sampled_probs = np.array(df['sampled_probs'].to_list())
-    df['e_u'] = np.sum(pure_probs ** 2, axis=1)
+    df['e_u'] = np.sum(pure_probs**2, axis=1)
     df['u_u'] = np.sum(pure_probs, axis=1) / D
     df['m_u'] = np.sum(pure_probs * sampled_probs, axis=1)
     df['y'] = df['m_u'] - df['u_u']
@@ -258,7 +258,7 @@ def test_characterize_phased_fsim_parameters_with_xeb():
 def test_parallel_full_workflow(use_pool):
     circuits = rqcg.generate_library_of_2q_circuits(
         n_library_circuits=5,
-        two_qubit_gate=cirq.ISWAP ** 0.5,
+        two_qubit_gate=cirq.ISWAP**0.5,
         max_cycle_depth=4,
         random_state=8675309,
     )
@@ -328,7 +328,7 @@ def test_parallel_full_workflow(use_pool):
 def test_fit_exponential_decays():
     rs = np.random.RandomState(999)
     cycle_depths = np.arange(3, 100, 11)
-    fidelities = 0.95 * 0.98 ** cycle_depths + rs.normal(0, 0.2)
+    fidelities = 0.95 * 0.98**cycle_depths + rs.normal(0, 0.2)
     a, layer_fid, a_std, layer_fid_std = _fit_exponential_decay(cycle_depths, fidelities)
     np.testing.assert_allclose([a, layer_fid], [0.95, 0.98], atol=0.02)
     assert 0 < a_std < 0.2 / len(cycle_depths)
@@ -338,7 +338,7 @@ def test_fit_exponential_decays():
 def test_fit_exponential_decays_negative_fids():
     rs = np.random.RandomState(999)
     cycle_depths = np.arange(3, 100, 11)
-    fidelities = 0.5 * 0.5 ** cycle_depths + rs.normal(0, 0.2) - 0.5
+    fidelities = 0.5 * 0.5**cycle_depths + rs.normal(0, 0.2) - 0.5
     assert np.sum(fidelities > 0) <= 1, 'they go negative'
     a, layer_fid, a_std, layer_fid_std = _fit_exponential_decay(cycle_depths, fidelities)
     assert a == 0
@@ -348,9 +348,9 @@ def test_fit_exponential_decays_negative_fids():
 
 
 def test_options_with_defaults_from_gate():
-    options = XEBPhasedFSimCharacterizationOptions().with_defaults_from_gate(cirq.ISWAP ** 0.5)
+    options = XEBPhasedFSimCharacterizationOptions().with_defaults_from_gate(cirq.ISWAP**0.5)
     np.testing.assert_allclose(options.theta_default, -np.pi / 4)
-    options = XEBPhasedFSimCharacterizationOptions().with_defaults_from_gate(cirq.ISWAP ** -0.5)
+    options = XEBPhasedFSimCharacterizationOptions().with_defaults_from_gate(cirq.ISWAP**-0.5)
     np.testing.assert_allclose(options.theta_default, np.pi / 4)
 
     options = XEBPhasedFSimCharacterizationOptions().with_defaults_from_gate(
diff --git a/cirq/experiments/xeb_sampling.py b/cirq/experiments/xeb_sampling.py
index 1200ccbb79b..3d4349cc73a 100644
--- a/cirq/experiments/xeb_sampling.py
+++ b/cirq/experiments/xeb_sampling.py
@@ -90,7 +90,7 @@ def __call__(self, tasks: List[_Sample2qXEBTask]) -> List[Dict[str, Any]]:
                 pair_measurement_key = str(pair_i)
                 pair = self.combinations_by_layer[task.layer_i].pairs[pair_i]
                 sampled_inds = result.data[pair_measurement_key].values
-                sampled_probs = np.bincount(sampled_inds, minlength=2 ** 2) / len(sampled_inds)
+                sampled_probs = np.bincount(sampled_inds, minlength=2**2) / len(sampled_inds)
 
                 records.append(
                     {
diff --git a/cirq/experiments/xeb_sampling_test.py b/cirq/experiments/xeb_sampling_test.py
index fcfad06022f..1aa731cd43a 100644
--- a/cirq/experiments/xeb_sampling_test.py
+++ b/cirq/experiments/xeb_sampling_test.py
@@ -105,7 +105,7 @@ def _assert_frame_approx_equal(df, df2, *, atol):
 
 def test_sample_2q_parallel_xeb_circuits(tmpdir):
     circuits = rqcg.generate_library_of_2q_circuits(
-        n_library_circuits=5, two_qubit_gate=cirq.ISWAP ** 0.5, max_cycle_depth=10
+        n_library_circuits=5, two_qubit_gate=cirq.ISWAP**0.5, max_cycle_depth=10
     )
     cycle_depths = [5, 10]
     graph = _gridqubits_to_graph_device(cirq.GridQubit.rect(3, 2))
@@ -149,7 +149,7 @@ def test_sample_2q_parallel_xeb_circuits(tmpdir):
 
 def test_sample_2q_parallel_xeb_circuits_bad_circuit_library():
     circuits = rqcg.generate_library_of_2q_circuits(
-        n_library_circuits=5, two_qubit_gate=cirq.ISWAP ** 0.5, max_cycle_depth=10
+        n_library_circuits=5, two_qubit_gate=cirq.ISWAP**0.5, max_cycle_depth=10
     )
     cycle_depths = [10]
     graph = _gridqubits_to_graph_device(cirq.GridQubit.rect(3, 2))
@@ -172,7 +172,7 @@ def test_sample_2q_parallel_xeb_circuits_bad_circuit_library():
 def test_sample_2q_parallel_xeb_circuits_error_bad_qubits():
     circuits = rqcg.generate_library_of_2q_circuits(
         n_library_circuits=5,
-        two_qubit_gate=cirq.ISWAP ** 0.5,
+        two_qubit_gate=cirq.ISWAP**0.5,
         max_cycle_depth=10,
         q0=cirq.GridQubit(0, 0),
         q1=cirq.GridQubit(1, 1),
diff --git a/cirq/interop/quirk/cells/composite_cell.py b/cirq/interop/quirk/cells/composite_cell.py
index c204ffb8aba..5b98cfb4bc4 100644
--- a/cirq/interop/quirk/cells/composite_cell.py
+++ b/cirq/interop/quirk/cells/composite_cell.py
@@ -117,7 +117,7 @@ def circuit(self) -> 'cirq.Circuit':
                 )
                 result += basis_change
                 result += body
-                result += basis_change ** -1
+                result += basis_change**-1
         return result
 
     def operations(self) -> 'cirq.OP_TREE':
diff --git a/cirq/interop/quirk/cells/control_cells.py b/cirq/interop/quirk/cells/control_cells.py
index 93d11e44ab6..dc0d8b85198 100644
--- a/cirq/interop/quirk/cells/control_cells.py
+++ b/cirq/interop/quirk/cells/control_cells.py
@@ -121,14 +121,14 @@ def generate_all_control_cell_makers() -> Iterator[CellMaker]:
     # Controls.
     yield _reg_control("•", basis_change=None)
     yield _reg_control("◦", basis_change=ops.X)
-    yield _reg_control("⊕", basis_change=ops.Y ** 0.5)
-    yield _reg_control("⊖", basis_change=ops.Y ** -0.5)
-    yield _reg_control("⊗", basis_change=ops.X ** -0.5)
-    yield _reg_control("(/)", basis_change=ops.X ** 0.5)
+    yield _reg_control("⊕", basis_change=ops.Y**0.5)
+    yield _reg_control("⊖", basis_change=ops.Y**-0.5)
+    yield _reg_control("⊗", basis_change=ops.X**-0.5)
+    yield _reg_control("(/)", basis_change=ops.X**0.5)
 
     # Parity controls.
-    yield _reg_parity_control("xpar", basis_change=ops.Y ** 0.5)
-    yield _reg_parity_control("ypar", basis_change=ops.X ** -0.5)
+    yield _reg_parity_control("xpar", basis_change=ops.Y**0.5)
+    yield _reg_parity_control("ypar", basis_change=ops.X**-0.5)
     yield _reg_parity_control("zpar", basis_change=None)
 
 
diff --git a/cirq/interop/quirk/cells/input_rotation_cells_test.py b/cirq/interop/quirk/cells/input_rotation_cells_test.py
index 3f93a2c7b8d..eb75d391231 100644
--- a/cirq/interop/quirk/cells/input_rotation_cells_test.py
+++ b/cirq/interop/quirk/cells/input_rotation_cells_test.py
@@ -37,7 +37,7 @@ def test_input_rotation_cells():
       │
 2: ───A1──────────
         """,
-        unitary=np.diag([1, 1, 1, 1, 1j ** 0, 1j ** 0.5, 1j ** 1, 1j ** 1.5]),
+        unitary=np.diag([1, 1, 1, 1, 1j**0, 1j**0.5, 1j**1, 1j**1.5]),
     )
     assert_url_to_circuit_returns(
         '{"cols":[["Z^(-A/2^n)","inputA1"]]}', unitary=np.diag([1, 1, 1, -1j])
@@ -45,20 +45,20 @@ def test_input_rotation_cells():
 
     assert_url_to_circuit_returns(
         '{"cols":[["H"],["X^(A/2^n)","inputA2"],["H"]]}',
-        unitary=np.diag([1, 1, 1, 1, 1j ** 0, 1j ** 0.5, 1j ** 1, 1j ** 1.5]),
+        unitary=np.diag([1, 1, 1, 1, 1j**0, 1j**0.5, 1j**1, 1j**1.5]),
     )
     assert_url_to_circuit_returns(
         '{"cols":[["H"],["X^(-A/2^n)","inputA2"],["H"]]}',
-        unitary=np.diag([1, 1, 1, 1, 1j ** 0, 1j ** -0.5, 1j ** -1, 1j ** -1.5]),
+        unitary=np.diag([1, 1, 1, 1, 1j**0, 1j**-0.5, 1j**-1, 1j**-1.5]),
     )
 
     assert_url_to_circuit_returns(
         '{"cols":[["X^-½"],["Y^(A/2^n)","inputA2"],["X^½"]]}',
-        unitary=np.diag([1, 1, 1, 1, 1j ** 0, 1j ** 0.5, 1j ** 1, 1j ** 1.5]),
+        unitary=np.diag([1, 1, 1, 1, 1j**0, 1j**0.5, 1j**1, 1j**1.5]),
     )
     assert_url_to_circuit_returns(
         '{"cols":[["X^-½"],["Y^(-A/2^n)","inputA2"],["X^½"]]}',
-        unitary=np.diag([1, 1, 1, 1, 1j ** 0, 1j ** -0.5, 1j ** -1, 1j ** -1.5]),
+        unitary=np.diag([1, 1, 1, 1, 1j**0, 1j**-0.5, 1j**-1, 1j**-1.5]),
     )
 
     assert_url_to_circuit_returns(
@@ -72,7 +72,7 @@ def test_input_rotation_cells():
       │
 3: ───A1──────────
         """,
-        unitary=np.diag([1 + 0j] * 13 + [1j ** 0.5, 1j, 1j ** 1.5]),
+        unitary=np.diag([1 + 0j] * 13 + [1j**0.5, 1j, 1j**1.5]),
     )
 
     assert_url_to_circuit_returns(
diff --git a/cirq/interop/quirk/cells/measurement_cells.py b/cirq/interop/quirk/cells/measurement_cells.py
index 1ccc668de55..5a2be8f9e5a 100644
--- a/cirq/interop/quirk/cells/measurement_cells.py
+++ b/cirq/interop/quirk/cells/measurement_cells.py
@@ -23,8 +23,8 @@
 def generate_all_measurement_cell_makers() -> Iterator[CellMaker]:
     yield _measurement("Measure")
     yield _measurement("ZDetector")
-    yield _measurement("YDetector", basis_change=ops.X ** -0.5)
-    yield _measurement("XDetector", basis_change=ops.Y ** 0.5)
+    yield _measurement("YDetector", basis_change=ops.X**-0.5)
+    yield _measurement("XDetector", basis_change=ops.Y**0.5)
 
 
 def _measurement(identifier: str, basis_change: Optional['cirq.Gate'] = None) -> CellMaker:
diff --git a/cirq/interop/quirk/cells/parse_test.py b/cirq/interop/quirk/cells/parse_test.py
index 0a3cbc332dc..2d9ad0b8235 100644
--- a/cirq/interop/quirk/cells/parse_test.py
+++ b/cirq/interop/quirk/cells/parse_test.py
@@ -85,7 +85,7 @@ def test_parse_complex():
     assert parse_complex('+i') == 1j
     assert parse_complex('1 + i - i') == 1
     assert parse_complex('1 + 2i - 3 i') == 1 - 1j
-    np.testing.assert_allclose(parse_complex('exp 2'), np.e ** 2, atol=1e-8)
+    np.testing.assert_allclose(parse_complex('exp 2'), np.e**2, atol=1e-8)
 
 
 def test_parse_complex_raw_cases_from_quirk():
diff --git a/cirq/interop/quirk/cells/scalar_cells.py b/cirq/interop/quirk/cells/scalar_cells.py
index 156c7516d8f..0236b354d78 100644
--- a/cirq/interop/quirk/cells/scalar_cells.py
+++ b/cirq/interop/quirk/cells/scalar_cells.py
@@ -24,7 +24,7 @@ def generate_all_scalar_cell_makers() -> Iterator[CellMaker]:
     yield _scalar("NeGate", ops.global_phase_operation(-1))
     yield _scalar("i", ops.global_phase_operation(1j))
     yield _scalar("-i", ops.global_phase_operation(-1j))
-    yield _scalar("√i", ops.global_phase_operation(1j ** 0.5))
+    yield _scalar("√i", ops.global_phase_operation(1j**0.5))
     yield _scalar("√-i", ops.global_phase_operation((-1j) ** 0.5))
 
 
diff --git a/cirq/interop/quirk/cells/scalar_cells_test.py b/cirq/interop/quirk/cells/scalar_cells_test.py
index 9e94209b8c5..648da7bc24a 100644
--- a/cirq/interop/quirk/cells/scalar_cells_test.py
+++ b/cirq/interop/quirk/cells/scalar_cells_test.py
@@ -30,9 +30,9 @@ def test_scalar_operations():
     )
 
     assert_url_to_circuit_returns(
-        '{"cols":[["√i"]]}', cirq.Circuit(cirq.global_phase_operation(1j ** 0.5))
+        '{"cols":[["√i"]]}', cirq.Circuit(cirq.global_phase_operation(1j**0.5))
     )
 
     assert_url_to_circuit_returns(
-        '{"cols":[["√-i"]]}', cirq.Circuit(cirq.global_phase_operation(1j ** -0.5))
+        '{"cols":[["√-i"]]}', cirq.Circuit(cirq.global_phase_operation(1j**-0.5))
     )
diff --git a/cirq/interop/quirk/cells/single_qubit_rotation_cells.py b/cirq/interop/quirk/cells/single_qubit_rotation_cells.py
index 73132382a22..cc4edd184bb 100644
--- a/cirq/interop/quirk/cells/single_qubit_rotation_cells.py
+++ b/cirq/interop/quirk/cells/single_qubit_rotation_cells.py
@@ -83,9 +83,9 @@ def generate_all_single_qubit_rotation_cell_makers() -> Iterator[CellMaker]:
     yield _gate("e^-iZt", ops.rz(-2 * sympy.pi * sympy.Symbol('t')))
 
     # Formulaic single qubit rotations.
-    yield _formula_gate("X^ft", "sin(pi*t)", lambda e: ops.X ** e)
-    yield _formula_gate("Y^ft", "sin(pi*t)", lambda e: ops.Y ** e)
-    yield _formula_gate("Z^ft", "sin(pi*t)", lambda e: ops.Z ** e)
+    yield _formula_gate("X^ft", "sin(pi*t)", lambda e: ops.X**e)
+    yield _formula_gate("Y^ft", "sin(pi*t)", lambda e: ops.Y**e)
+    yield _formula_gate("Z^ft", "sin(pi*t)", lambda e: ops.Z**e)
     yield _formula_gate("Rxft", "pi*t*t", ops.rx)
     yield _formula_gate("Ryft", "pi*t*t", ops.ry)
     yield _formula_gate("Rzft", "pi*t*t", ops.rz)
diff --git a/cirq/interop/quirk/url_to_circuit.py b/cirq/interop/quirk/url_to_circuit.py
index dae7b14f663..4007e0722ac 100644
--- a/cirq/interop/quirk/url_to_circuit.py
+++ b/cirq/interop/quirk/url_to_circuit.py
@@ -51,7 +51,7 @@ def quirk_url_to_circuit(
     extra_cell_makers: Union[
         Dict[str, 'cirq.Gate'], Iterable['cirq.interop.quirk.cells.CellMaker']
     ] = (),
-    max_operation_count: int = 10 ** 6,
+    max_operation_count: int = 10**6,
 ) -> 'cirq.Circuit':
     """Parses a Cirq circuit out of a Quirk URL.
 
@@ -154,7 +154,7 @@ def quirk_json_to_circuit(
         Dict[str, 'cirq.Gate'], Iterable['cirq.interop.quirk.cells.CellMaker']
     ] = (),
     quirk_url: Optional[str] = None,
-    max_operation_count: int = 10 ** 6,
+    max_operation_count: int = 10**6,
 ) -> 'cirq.Circuit':
     """Constructs a Cirq circuit from Quirk's JSON format.
 
diff --git a/cirq/interop/quirk/url_to_circuit_test.py b/cirq/interop/quirk/url_to_circuit_test.py
index 1762dd18cb0..2205c53870f 100644
--- a/cirq/interop/quirk/url_to_circuit_test.py
+++ b/cirq/interop/quirk/url_to_circuit_test.py
@@ -83,21 +83,15 @@ def test_parse_with_qubits():
     b = cirq.GridQubit(0, 1)
     c = cirq.GridQubit(0, 2)
 
-    assert (
-        quirk_url_to_circuit(
-            'http://algassert.com/quirk#circuit={"cols":[["H"],["•","X"]]}',
-            qubits=cirq.GridQubit.rect(4, 4),
-        )
-        == cirq.Circuit(cirq.H(a), cirq.X(b).controlled_by(a))
-    )
+    assert quirk_url_to_circuit(
+        'http://algassert.com/quirk#circuit={"cols":[["H"],["•","X"]]}',
+        qubits=cirq.GridQubit.rect(4, 4),
+    ) == cirq.Circuit(cirq.H(a), cirq.X(b).controlled_by(a))
 
-    assert (
-        quirk_url_to_circuit(
-            'http://algassert.com/quirk#circuit={"cols":[["H"],["•",1,"X"]]}',
-            qubits=cirq.GridQubit.rect(4, 4),
-        )
-        == cirq.Circuit(cirq.H(a), cirq.X(c).controlled_by(a))
-    )
+    assert quirk_url_to_circuit(
+        'http://algassert.com/quirk#circuit={"cols":[["H"],["•",1,"X"]]}',
+        qubits=cirq.GridQubit.rect(4, 4),
+    ) == cirq.Circuit(cirq.H(a), cirq.X(c).controlled_by(a))
 
     with pytest.raises(IndexError, match="qubits specified"):
         _ = quirk_url_to_circuit(
@@ -107,25 +101,19 @@ def test_parse_with_qubits():
 
 
 def test_extra_cell_makers():
-    assert (
-        cirq.quirk_url_to_circuit(
-            'http://algassert.com/quirk#circuit={"cols":[["iswap"]]}',
-            extra_cell_makers=[
-                cirq.interop.quirk.cells.CellMaker(
-                    identifier='iswap', size=2, maker=lambda args: cirq.ISWAP(*args.qubits)
-                )
-            ],
-        )
-        == cirq.Circuit(cirq.ISWAP(*cirq.LineQubit.range(2)))
-    )
+    assert cirq.quirk_url_to_circuit(
+        'http://algassert.com/quirk#circuit={"cols":[["iswap"]]}',
+        extra_cell_makers=[
+            cirq.interop.quirk.cells.CellMaker(
+                identifier='iswap', size=2, maker=lambda args: cirq.ISWAP(*args.qubits)
+            )
+        ],
+    ) == cirq.Circuit(cirq.ISWAP(*cirq.LineQubit.range(2)))
 
-    assert (
-        cirq.quirk_url_to_circuit(
-            'http://algassert.com/quirk#circuit={"cols":[["iswap"]]}',
-            extra_cell_makers={'iswap': cirq.ISWAP},
-        )
-        == cirq.Circuit(cirq.ISWAP(*cirq.LineQubit.range(2)))
-    )
+    assert cirq.quirk_url_to_circuit(
+        'http://algassert.com/quirk#circuit={"cols":[["iswap"]]}',
+        extra_cell_makers={'iswap': cirq.ISWAP},
+    ) == cirq.Circuit(cirq.ISWAP(*cirq.LineQubit.range(2)))
 
     assert cirq.quirk_url_to_circuit(
         'http://algassert.com/quirk#circuit={"cols":[["iswap"], ["toffoli"]]}',
@@ -327,7 +315,7 @@ def test_survives_a_billion_laughs():
             '{"id":"~y","circuit":{"cols":[["~x"],["~x"],["~x"],["~x"]]}},'
             '{"id":"~z","circuit":{"cols":[["~y"],["~y"],["~y"],["~y"]]}}'
             ']}',
-            max_operation_count=10 ** 6,
+            max_operation_count=10**6,
         )
 
 
diff --git a/cirq/ion/ion_decomposition.py b/cirq/ion/ion_decomposition.py
index 81c88bbd919..691780e1115 100644
--- a/cirq/ion/ion_decomposition.py
+++ b/cirq/ion/ion_decomposition.py
@@ -118,6 +118,6 @@ def _non_local_part(
 
     return [
         _parity_interaction(q0, q1, x, atol),
-        _parity_interaction(q0, q1, y, atol, ops.Z ** -0.5),
-        _parity_interaction(q0, q1, z, atol, ops.Y ** 0.5),
+        _parity_interaction(q0, q1, y, atol, ops.Z**-0.5),
+        _parity_interaction(q0, q1, z, atol, ops.Y**0.5),
     ]
diff --git a/cirq/ion/ion_gates_test.py b/cirq/ion/ion_gates_test.py
index e94c9e9255e..538abb20f0c 100644
--- a/cirq/ion/ion_gates_test.py
+++ b/cirq/ion/ion_gates_test.py
@@ -27,9 +27,9 @@ def test_ms_str():
     ms = cirq.ms(np.pi / 2)
     assert str(ms) == 'MS(π/2)'
     assert str(cirq.ms(np.pi)) == 'MS(2.0π/2)'
-    assert str(ms ** 0.5) == 'MS(0.5π/2)'
-    assert str(ms ** 2) == 'MS(2.0π/2)'
-    assert str(ms ** -1) == 'MS(-1.0π/2)'
+    assert str(ms**0.5) == 'MS(0.5π/2)'
+    assert str(ms**2) == 'MS(2.0π/2)'
+    assert str(ms**-1) == 'MS(-1.0π/2)'
 
 
 def test_ms_matrix():
@@ -50,8 +50,8 @@ def test_ms_repr():
     assert repr(cirq.ms(np.pi / 4)) == 'cirq.ms(0.5*np.pi/2)'
     cirq.testing.assert_equivalent_repr(cirq.ms(np.pi / 4))
     ms = cirq.ms(np.pi / 2)
-    assert repr(ms ** 2) == 'cirq.ms(2.0*np.pi/2)'
-    assert repr(ms ** -0.5) == 'cirq.ms(-0.5*np.pi/2)'
+    assert repr(ms**2) == 'cirq.ms(2.0*np.pi/2)'
+    assert repr(ms**-0.5) == 'cirq.ms(-0.5*np.pi/2)'
 
 
 def test_ms_diagrams():
diff --git a/cirq/linalg/decompositions.py b/cirq/linalg/decompositions.py
index 163d51b9946..7248dd4ec32 100644
--- a/cirq/linalg/decompositions.py
+++ b/cirq/linalg/decompositions.py
@@ -726,7 +726,7 @@ def kak_canonicalize_vector(x: float, y: float, z: float, atol: float = 1e-9) ->
     # Shifting strength by ½π is equivalent to local ops (e.g. exp(i½π XX)∝XX).
     def shift(k, step):
         v[k] += step * np.pi / 2
-        phase[0] *= 1j ** step
+        phase[0] *= 1j**step
         right[0] = combinators.dot(flippers[k] ** (step % 4), right[0])
         right[1] = combinators.dot(flippers[k] ** (step % 4), right[1])
 
diff --git a/cirq/linalg/decompositions_test.py b/cirq/linalg/decompositions_test.py
index 855ed96f565..8b1f255f085 100644
--- a/cirq/linalg/decompositions_test.py
+++ b/cirq/linalg/decompositions_test.py
@@ -425,13 +425,13 @@ def test_axis_angle_decomposition_str():
     assert str(cirq.axis_angle(cirq.unitary(cirq.Y))) == '1*π around Y'
     assert str(cirq.axis_angle(cirq.unitary(cirq.Z))) == '1*π around Z'
     assert str(cirq.axis_angle(cirq.unitary(cirq.H))) == '1*π around 0.707*X+0.707*Z'
-    assert str(cirq.axis_angle(cirq.unitary(cirq.H ** 0.5))) == '0.5*π around 0.707*X+0.707*Z'
+    assert str(cirq.axis_angle(cirq.unitary(cirq.H**0.5))) == '0.5*π around 0.707*X+0.707*Z'
     assert (
         str(
             cirq.axis_angle(
-                cirq.unitary(cirq.X ** 0.25)
-                @ cirq.unitary(cirq.Y ** 0.25)
-                @ cirq.unitary(cirq.Z ** 0.25)
+                cirq.unitary(cirq.X**0.25)
+                @ cirq.unitary(cirq.Y**0.25)
+                @ cirq.unitary(cirq.Z**0.25)
             )
         )
         == '0.477*π around 0.679*X+0.281*Y+0.679*Z'
@@ -462,14 +462,14 @@ def test_axis_angle():
         atol=1e-8,
     )
     assert cirq.approx_eq(
-        cirq.axis_angle(cirq.unitary(cirq.X ** 0.5)),
+        cirq.axis_angle(cirq.unitary(cirq.X**0.5)),
         cirq.AxisAngleDecomposition(
             angle=np.pi / 2, axis=(1, 0, 0), global_phase=np.exp(1j * np.pi / 4)
         ),
         atol=1e-8,
     )
     assert cirq.approx_eq(
-        cirq.axis_angle(cirq.unitary(cirq.X ** -0.5)),
+        cirq.axis_angle(cirq.unitary(cirq.X**-0.5)),
         cirq.AxisAngleDecomposition(
             angle=-np.pi / 2, axis=(1, 0, 0), global_phase=np.exp(-1j * np.pi / 4)
         ),
@@ -496,7 +496,7 @@ def test_axis_angle():
     )
 
     assert cirq.approx_eq(
-        cirq.axis_angle(cirq.unitary(cirq.H ** 0.5)),
+        cirq.axis_angle(cirq.unitary(cirq.H**0.5)),
         cirq.AxisAngleDecomposition(
             angle=np.pi / 2,
             axis=(np.sqrt(0.5), 0, np.sqrt(0.5)),
@@ -736,9 +736,9 @@ def test_kak_vector_input_not_unitary():
         cirq.testing.random_unitary(4),
         cirq.unitary(cirq.IdentityGate(2)),
         cirq.unitary(cirq.SWAP),
-        cirq.unitary(cirq.SWAP ** 0.25),
+        cirq.unitary(cirq.SWAP**0.25),
         cirq.unitary(cirq.ISWAP),
-        cirq.unitary(cirq.CZ ** 0.5),
+        cirq.unitary(cirq.CZ**0.5),
         cirq.unitary(cirq.CZ),
     ],
 )
diff --git a/cirq/linalg/operator_spaces_test.py b/cirq/linalg/operator_spaces_test.py
index 27decca0627..3070c8ec4df 100644
--- a/cirq/linalg/operator_spaces_test.py
+++ b/cirq/linalg/operator_spaces_test.py
@@ -123,7 +123,7 @@ def test_kron_bases_consistency(basis1, basis2):
 @pytest.mark.parametrize('basis,repeat', itertools.product((PAULI_BASIS, STANDARD_BASIS), range(5)))
 def test_kron_bases_repeat_sanity_checks(basis, repeat):
     product_basis = cirq.kron_bases(basis, repeat=repeat)
-    assert len(product_basis) == 4 ** repeat
+    assert len(product_basis) == 4**repeat
     for name1, matrix1 in product_basis.items():
         for name2, matrix2 in product_basis.items():
             p = cirq.hilbert_schmidt_inner_product(matrix1, matrix2)
diff --git a/cirq/linalg/transformations.py b/cirq/linalg/transformations.py
index 614a34940f1..d407ffe57e2 100644
--- a/cirq/linalg/transformations.py
+++ b/cirq/linalg/transformations.py
@@ -368,7 +368,7 @@ def partial_trace_of_state_vector_as_mixture(
 
     if state_vector.ndim == 1:
         dims = int(np.log2(state_vector.size))
-        if 2 ** dims != state_vector.size:
+        if 2**dims != state_vector.size:
             raise ValueError(f'Cannot infer underlying shape of {state_vector.shape}.')
         state_vector = state_vector.reshape((2,) * dims)
         ret_shape: Tuple[int, ...] = (2 ** len(keep_indices),)
diff --git a/cirq/linalg/transformations_test.py b/cirq/linalg/transformations_test.py
index 3303aec9935..d9f5175e18c 100644
--- a/cirq/linalg/transformations_test.py
+++ b/cirq/linalg/transformations_test.py
@@ -547,7 +547,7 @@ def test_partial_trace_of_state_vector_as_mixture_pure_result():
     )
 
     # Shapes of states in the output mixture conform to the input's shape.
-    state = state.reshape(2 ** 9)
+    state = state.reshape(2**9)
     assert mixtures_equal(
         cirq.partial_trace_of_state_vector_as_mixture(state, [0, 1], atol=1e-8), ((1.0, a),)
     )
diff --git a/cirq/neutral_atoms/neutral_atom_devices_test.py b/cirq/neutral_atoms/neutral_atom_devices_test.py
index a1a410ddd0f..1a3d6f0eb86 100644
--- a/cirq/neutral_atoms/neutral_atom_devices_test.py
+++ b/cirq/neutral_atoms/neutral_atom_devices_test.py
@@ -23,8 +23,8 @@
 def square_device(
     width: int, height: int, holes=(), max_controls=2, use_timedelta=False
 ) -> neutral_atoms.NeutralAtomDevice:
-    us = cirq.Duration(nanos=10 ** 3) if not use_timedelta else timedelta(microseconds=1)
-    ms = cirq.Duration(nanos=10 ** 6) if not use_timedelta else timedelta(microseconds=1000)
+    us = cirq.Duration(nanos=10**3) if not use_timedelta else timedelta(microseconds=1)
+    ms = cirq.Duration(nanos=10**6) if not use_timedelta else timedelta(microseconds=1000)
     return neutral_atoms.NeutralAtomDevice(  # type: ignore
         measurement_duration=50 * ms,  # type: ignore
         gate_duration=100 * us,  # type: ignore
@@ -43,8 +43,8 @@ def square_device(
 
 def test_init():
     d = square_device(2, 2, holes=[cirq.GridQubit(1, 1)])
-    us = cirq.Duration(nanos=10 ** 3)
-    ms = cirq.Duration(nanos=10 ** 6)
+    us = cirq.Duration(nanos=10**3)
+    ms = cirq.Duration(nanos=10**6)
     q00 = cirq.GridQubit(0, 0)
     q01 = cirq.GridQubit(0, 1)
     q10 = cirq.GridQubit(1, 0)
@@ -73,8 +73,8 @@ def test_metadata():
 
 def test_init_timedelta():
     d = square_device(2, 2, holes=[cirq.GridQubit(1, 1)], use_timedelta=True)
-    us = cirq.Duration(nanos=10 ** 3)
-    ms = cirq.Duration(nanos=10 ** 6)
+    us = cirq.Duration(nanos=10**3)
+    ms = cirq.Duration(nanos=10**6)
     q00 = cirq.GridQubit(0, 0)
     q01 = cirq.GridQubit(0, 1)
     q10 = cirq.GridQubit(1, 0)
@@ -88,8 +88,8 @@ def test_init_timedelta():
 
 def test_init_errors():
     line = cirq.LineQubit.range(3)
-    us = cirq.Duration(nanos=10 ** 3)
-    ms = cirq.Duration(nanos=10 ** 6)
+    us = cirq.Duration(nanos=10**3)
+    ms = cirq.Duration(nanos=10**6)
     with pytest.raises(ValueError, match="Unsupported qubit type"):
         _ = neutral_atoms.NeutralAtomDevice(
             measurement_duration=50 * ms,
@@ -115,7 +115,7 @@ def test_init_errors():
 def test_decompose_error_deprecated():
     d = square_device(2, 2, holes=[cirq.GridQubit(1, 1)])
     with cirq.testing.assert_deprecated('ConvertToNeutralAtomGates', deadline='v0.15'):
-        for op in d.decompose_operation((cirq.CCZ ** 1.5).on(*(d.qubit_list()))):
+        for op in d.decompose_operation((cirq.CCZ**1.5).on(*(d.qubit_list()))):
             d.validate_operation(op)
 
 
@@ -176,7 +176,7 @@ def test_validate_moment_errors():
     q20 = cirq.GridQubit(2, 0)
     q21 = cirq.GridQubit(2, 1)
 
-    m = cirq.Moment([cirq.Z.on(q00), (cirq.Z ** 2).on(q01)])
+    m = cirq.Moment([cirq.Z.on(q00), (cirq.Z**2).on(q01)])
     with pytest.raises(ValueError, match="Non-identical simultaneous "):
         d.validate_moment(m)
     m = cirq.Moment([cirq.X.on(q00), cirq.Y.on(q01)])
@@ -206,8 +206,8 @@ def test_validate_moment_errors():
     ):
         d.validate_moment(m)
     d.validate_moment(cirq.Moment([cirq.X.on(q00), cirq.Z.on(q01)]))
-    us = cirq.Duration(nanos=10 ** 3)
-    ms = cirq.Duration(nanos=10 ** 6)
+    us = cirq.Duration(nanos=10**3)
+    ms = cirq.Duration(nanos=10**6)
     d2 = neutral_atoms.NeutralAtomDevice(
         measurement_duration=50 * ms,
         gate_duration=100 * us,
diff --git a/cirq/ops/boolean_hamiltonian_test.py b/cirq/ops/boolean_hamiltonian_test.py
index 4932450836d..420131ca05b 100644
--- a/cirq/ops/boolean_hamiltonian_test.py
+++ b/cirq/ops/boolean_hamiltonian_test.py
@@ -150,7 +150,7 @@ def test_gate_consistent():
 )
 def test_gray_code_sorting(n_bits, expected_hs):
     hs_template = []
-    for x in range(2 ** n_bits):
+    for x in range(2**n_bits):
         h = []
         for i in range(n_bits):
             if x % 2 == 1:
diff --git a/cirq/ops/clifford_gate.py b/cirq/ops/clifford_gate.py
index 91649fdc1aa..4035770113e 100644
--- a/cirq/ops/clifford_gate.py
+++ b/cirq/ops/clifford_gate.py
@@ -487,7 +487,7 @@ def equivalent_gate_before(self, after: 'SingleQubitCliffordGate') -> 'SingleQub
         """Returns a SingleQubitCliffordGate such that the circuits
             --output--self-- and --self--gate--
         are equivalent up to global phase."""
-        return self.merged_with(after).merged_with(self ** -1)
+        return self.merged_with(after).merged_with(self**-1)
 
     def __repr__(self) -> str:
         x = self.transform(pauli_gates.X)
diff --git a/cirq/ops/clifford_gate_test.py b/cirq/ops/clifford_gate_test.py
index 1a4424f0435..4aa8db2f90d 100644
--- a/cirq/ops/clifford_gate_test.py
+++ b/cirq/ops/clifford_gate_test.py
@@ -148,7 +148,7 @@ def test_init_90rot_from_single(trans, frm):
     # Check that flipping the transform produces the inverse rotation
     trans_rev = cirq.PauliTransform(trans.to, not trans.flip)
     gate_rev = cirq.SingleQubitCliffordGate.from_single_map({frm: trans_rev})
-    assert gate ** -1 == gate_rev
+    assert gate**-1 == gate_rev
 
 
 @pytest.mark.parametrize(
@@ -206,20 +206,20 @@ def test_init_from_pauli(pauli, sqrt, expected):
 
 
 def test_pow():
-    assert cirq.SingleQubitCliffordGate.X ** -1 == cirq.SingleQubitCliffordGate.X
-    assert cirq.SingleQubitCliffordGate.H ** -1 == cirq.SingleQubitCliffordGate.H
-    assert cirq.SingleQubitCliffordGate.X_sqrt == cirq.SingleQubitCliffordGate.X ** 0.5
-    assert cirq.SingleQubitCliffordGate.Y_sqrt == cirq.SingleQubitCliffordGate.Y ** 0.5
-    assert cirq.SingleQubitCliffordGate.Z_sqrt == cirq.SingleQubitCliffordGate.Z ** 0.5
-    assert cirq.SingleQubitCliffordGate.X_nsqrt == cirq.SingleQubitCliffordGate.X ** -0.5
-    assert cirq.SingleQubitCliffordGate.Y_nsqrt == cirq.SingleQubitCliffordGate.Y ** -0.5
-    assert cirq.SingleQubitCliffordGate.Z_nsqrt == cirq.SingleQubitCliffordGate.Z ** -0.5
-    assert cirq.SingleQubitCliffordGate.X_sqrt ** -1 == cirq.SingleQubitCliffordGate.X_nsqrt
+    assert cirq.SingleQubitCliffordGate.X**-1 == cirq.SingleQubitCliffordGate.X
+    assert cirq.SingleQubitCliffordGate.H**-1 == cirq.SingleQubitCliffordGate.H
+    assert cirq.SingleQubitCliffordGate.X_sqrt == cirq.SingleQubitCliffordGate.X**0.5
+    assert cirq.SingleQubitCliffordGate.Y_sqrt == cirq.SingleQubitCliffordGate.Y**0.5
+    assert cirq.SingleQubitCliffordGate.Z_sqrt == cirq.SingleQubitCliffordGate.Z**0.5
+    assert cirq.SingleQubitCliffordGate.X_nsqrt == cirq.SingleQubitCliffordGate.X**-0.5
+    assert cirq.SingleQubitCliffordGate.Y_nsqrt == cirq.SingleQubitCliffordGate.Y**-0.5
+    assert cirq.SingleQubitCliffordGate.Z_nsqrt == cirq.SingleQubitCliffordGate.Z**-0.5
+    assert cirq.SingleQubitCliffordGate.X_sqrt**-1 == cirq.SingleQubitCliffordGate.X_nsqrt
     assert cirq.inverse(cirq.SingleQubitCliffordGate.X_nsqrt) == (
         cirq.SingleQubitCliffordGate.X_sqrt
     )
     with pytest.raises(TypeError):
-        _ = cirq.SingleQubitCliffordGate.Z ** 0.25
+        _ = cirq.SingleQubitCliffordGate.Z**0.25
 
 
 def test_init_from_quarter_turns():
@@ -353,17 +353,17 @@ def test_y_rotation(gate, trans_y):
 @pytest.mark.parametrize(
     'gate,gate_equiv',
     (
-        (cirq.SingleQubitCliffordGate.I, cirq.X ** 0),
+        (cirq.SingleQubitCliffordGate.I, cirq.X**0),
         (cirq.SingleQubitCliffordGate.H, cirq.H),
         (cirq.SingleQubitCliffordGate.X, cirq.X),
         (cirq.SingleQubitCliffordGate.Y, cirq.Y),
         (cirq.SingleQubitCliffordGate.Z, cirq.Z),
-        (cirq.SingleQubitCliffordGate.X_sqrt, cirq.X ** 0.5),
-        (cirq.SingleQubitCliffordGate.X_nsqrt, cirq.X ** -0.5),
-        (cirq.SingleQubitCliffordGate.Y_sqrt, cirq.Y ** 0.5),
-        (cirq.SingleQubitCliffordGate.Y_nsqrt, cirq.Y ** -0.5),
-        (cirq.SingleQubitCliffordGate.Z_sqrt, cirq.Z ** 0.5),
-        (cirq.SingleQubitCliffordGate.Z_nsqrt, cirq.Z ** -0.5),
+        (cirq.SingleQubitCliffordGate.X_sqrt, cirq.X**0.5),
+        (cirq.SingleQubitCliffordGate.X_nsqrt, cirq.X**-0.5),
+        (cirq.SingleQubitCliffordGate.Y_sqrt, cirq.Y**0.5),
+        (cirq.SingleQubitCliffordGate.Y_nsqrt, cirq.Y**-0.5),
+        (cirq.SingleQubitCliffordGate.Z_sqrt, cirq.Z**0.5),
+        (cirq.SingleQubitCliffordGate.Z_nsqrt, cirq.Z**-0.5),
     ),
 )
 def test_decompose(gate, gate_equiv):
@@ -378,17 +378,17 @@ def test_decompose(gate, gate_equiv):
 @pytest.mark.parametrize(
     'gate,gate_equiv',
     (
-        (cirq.SingleQubitCliffordGate.I, cirq.X ** 0),
+        (cirq.SingleQubitCliffordGate.I, cirq.X**0),
         (cirq.SingleQubitCliffordGate.H, cirq.H),
         (cirq.SingleQubitCliffordGate.X, cirq.X),
         (cirq.SingleQubitCliffordGate.Y, cirq.Y),
         (cirq.SingleQubitCliffordGate.Z, cirq.Z),
-        (cirq.SingleQubitCliffordGate.X_sqrt, cirq.X ** 0.5),
-        (cirq.SingleQubitCliffordGate.X_nsqrt, cirq.X ** -0.5),
-        (cirq.SingleQubitCliffordGate.Y_sqrt, cirq.Y ** 0.5),
-        (cirq.SingleQubitCliffordGate.Y_nsqrt, cirq.Y ** -0.5),
-        (cirq.SingleQubitCliffordGate.Z_sqrt, cirq.Z ** 0.5),
-        (cirq.SingleQubitCliffordGate.Z_nsqrt, cirq.Z ** -0.5),
+        (cirq.SingleQubitCliffordGate.X_sqrt, cirq.X**0.5),
+        (cirq.SingleQubitCliffordGate.X_nsqrt, cirq.X**-0.5),
+        (cirq.SingleQubitCliffordGate.Y_sqrt, cirq.Y**0.5),
+        (cirq.SingleQubitCliffordGate.Y_nsqrt, cirq.Y**-0.5),
+        (cirq.SingleQubitCliffordGate.Z_sqrt, cirq.Z**0.5),
+        (cirq.SingleQubitCliffordGate.Z_nsqrt, cirq.Z**-0.5),
     ),
 )
 def test_known_matrix(gate, gate_equiv):
@@ -459,7 +459,7 @@ def test_parses_single_qubit_gate(gate):
 )
 def test_commutes_pauli(gate, pauli, half_turns):
     # TODO(#4328) cirq.X**1 should be _PauliX instead of XPowGate
-    pauli_gate = pauli if half_turns == 1 else pauli ** half_turns
+    pauli_gate = pauli if half_turns == 1 else pauli**half_turns
     q0 = cirq.NamedQubit('q0')
     mat = cirq.Circuit(
         gate(q0),
@@ -589,7 +589,7 @@ def test_from_xz_to_clifford_tableau():
     seen_tableau = []
     for trans_x, trans_z in _all_rotation_pairs():
         tableau = cirq.SingleQubitCliffordGate.from_xz_map(trans_x, trans_z).clifford_tableau
-        tableau_number = sum(2 ** i * t for i, t in enumerate(tableau.matrix().ravel()))
+        tableau_number = sum(2**i * t for i, t in enumerate(tableau.matrix().ravel()))
         tableau_number = tableau_number * 4 + 2 * tableau.rs[0] + tableau.rs[1]
         seen_tableau.append(tableau_number)
         # Satisfy the symplectic property
@@ -630,15 +630,15 @@ def test_common_clifford_gate_caching(clifford_gate_name):
 
 
 def test_multi_qubit_clifford_pow():
-    assert cirq.CliffordGate.X ** -1 == cirq.CliffordGate.X
-    assert cirq.CliffordGate.H ** -1 == cirq.CliffordGate.H
-    assert cirq.CliffordGate.S ** 2 == cirq.CliffordGate.Z
-    assert cirq.CliffordGate.S ** -1 == cirq.CliffordGate.S ** 3
-    assert cirq.CliffordGate.S ** -3 == cirq.CliffordGate.S
-    assert cirq.CliffordGate.CNOT ** 3 == cirq.CliffordGate.CNOT
-    assert cirq.CliffordGate.CNOT ** -3 == cirq.CliffordGate.CNOT
+    assert cirq.CliffordGate.X**-1 == cirq.CliffordGate.X
+    assert cirq.CliffordGate.H**-1 == cirq.CliffordGate.H
+    assert cirq.CliffordGate.S**2 == cirq.CliffordGate.Z
+    assert cirq.CliffordGate.S**-1 == cirq.CliffordGate.S**3
+    assert cirq.CliffordGate.S**-3 == cirq.CliffordGate.S
+    assert cirq.CliffordGate.CNOT**3 == cirq.CliffordGate.CNOT
+    assert cirq.CliffordGate.CNOT**-3 == cirq.CliffordGate.CNOT
     with pytest.raises(TypeError):
-        _ = cirq.CliffordGate.Z ** 0.25
+        _ = cirq.CliffordGate.Z**0.25
 
 
 def test_stabilizer_effec():
diff --git a/cirq/ops/common_channels.py b/cirq/ops/common_channels.py
index 753db55dc78..8b5ec1c5bc2 100644
--- a/cirq/ops/common_channels.py
+++ b/cirq/ops/common_channels.py
@@ -280,7 +280,7 @@ def __init__(self, p: float, n_qubits: int = 1) -> None:
 
         error_probabilities = {}
 
-        p_depol = p / (4 ** n_qubits - 1)
+        p_depol = p / (4**n_qubits - 1)
         p_identity = 1.0 - p
         for pauli_tuple in itertools.product(['I', 'X', 'Y', 'Z'], repeat=n_qubits):
             pauli_string = ''.join(pauli_tuple)
diff --git a/cirq/ops/common_gate_families_test.py b/cirq/ops/common_gate_families_test.py
index 6c78e128713..5c2a25a72c4 100644
--- a/cirq/ops/common_gate_families_test.py
+++ b/cirq/ops/common_gate_families_test.py
@@ -65,8 +65,8 @@ def test_any_integer_power_gate_family():
     eq.add_equality_group(cirq.AnyIntegerPowerGateFamily(cirq.EigenGate))
     cirq.testing.assert_equivalent_repr(gate_family)
     assert CustomX in gate_family
-    assert CustomX ** 2 in gate_family
-    assert CustomX ** 1.5 not in gate_family
+    assert CustomX**2 in gate_family
+    assert CustomX**1.5 not in gate_family
     assert CustomX ** sympy.Symbol('theta') not in gate_family
     assert 'CustomXPowGate' in gate_family.name
     assert '`g.exponent` is an integer' in gate_family.description
diff --git a/cirq/ops/common_gates.py b/cirq/ops/common_gates.py
index 75938f9a385..9ceebe1424c 100644
--- a/cirq/ops/common_gates.py
+++ b/cirq/ops/common_gates.py
@@ -908,7 +908,7 @@ def _pauli_expansion_(self) -> value.LinearDict[str]:
         if protocols.is_parameterized(self):
             return NotImplemented
         global_phase = 1j ** (2 * self._exponent * self._global_shift)
-        z_phase = 1j ** self._exponent
+        z_phase = 1j**self._exponent
         c = -1j * z_phase * np.sin(np.pi * self._exponent / 2) / 2
         return value.LinearDict(
             {
@@ -1090,7 +1090,7 @@ def _pauli_expansion_(self) -> value.LinearDict[str]:
         if protocols.is_parameterized(self):
             return NotImplemented
         global_phase = 1j ** (2 * self._exponent * self._global_shift)
-        cnot_phase = 1j ** self._exponent
+        cnot_phase = 1j**self._exponent
         c = -1j * cnot_phase * np.sin(np.pi * self._exponent / 2) / 2
         return value.LinearDict(
             {
diff --git a/cirq/ops/common_gates_test.py b/cirq/ops/common_gates_test.py
index f22af2f7501..8e59fa66921 100644
--- a/cirq/ops/common_gates_test.py
+++ b/cirq/ops/common_gates_test.py
@@ -53,7 +53,7 @@ def test_phase_sensitive_eigen_gates_consistent_protocols(eigen_gate_type):
 def test_cz_init():
     assert cirq.CZPowGate(exponent=0.5).exponent == 0.5
     assert cirq.CZPowGate(exponent=5).exponent == 5
-    assert (cirq.CZ ** 0.5).exponent == 0.5
+    assert (cirq.CZ**0.5).exponent == 0.5
 
 
 @pytest.mark.parametrize('theta,pi', [(0.4, np.pi), (sympy.Symbol("theta"), sympy.pi)])
@@ -80,14 +80,14 @@ def test_transformations(theta, pi):
 
 def test_cz_str():
     assert str(cirq.CZ) == 'CZ'
-    assert str(cirq.CZ ** 0.5) == 'CZ**0.5'
-    assert str(cirq.CZ ** -0.25) == 'CZ**-0.25'
+    assert str(cirq.CZ**0.5) == 'CZ**0.5'
+    assert str(cirq.CZ**-0.25) == 'CZ**-0.25'
 
 
 def test_cz_repr():
     assert repr(cirq.CZ) == 'cirq.CZ'
-    assert repr(cirq.CZ ** 0.5) == '(cirq.CZ**0.5)'
-    assert repr(cirq.CZ ** -0.25) == '(cirq.CZ**-0.25)'
+    assert repr(cirq.CZ**0.5) == '(cirq.CZ**0.5)'
+    assert repr(cirq.CZ**-0.25) == '(cirq.CZ**-0.25)'
 
 
 def test_cz_unitary():
@@ -96,17 +96,17 @@ def test_cz_unitary():
     )
 
     assert np.allclose(
-        cirq.unitary(cirq.CZ ** 0.5),
+        cirq.unitary(cirq.CZ**0.5),
         np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1j]]),
     )
 
     assert np.allclose(
-        cirq.unitary(cirq.CZ ** 0),
+        cirq.unitary(cirq.CZ**0),
         np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]),
     )
 
     assert np.allclose(
-        cirq.unitary(cirq.CZ ** -0.5),
+        cirq.unitary(cirq.CZ**-0.5),
         np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1j]]),
     )
 
@@ -116,9 +116,9 @@ def test_z_init():
     assert z.exponent == 5
 
     # Canonicalizes exponent for equality, but keeps the inner details.
-    assert cirq.Z ** 0.5 != cirq.Z ** -0.5
-    assert (cirq.Z ** -1) ** 0.5 == cirq.Z ** -0.5
-    assert cirq.Z ** -1 == cirq.Z
+    assert cirq.Z**0.5 != cirq.Z**-0.5
+    assert (cirq.Z**-1) ** 0.5 == cirq.Z**-0.5
+    assert cirq.Z**-1 == cirq.Z
 
 
 @pytest.mark.parametrize(
@@ -222,11 +222,11 @@ def test_global_phase_controlled_gate(gate, matrix):
 def test_rot_gates_eq():
     eq = cirq.testing.EqualsTester()
     gates = [
-        lambda p: cirq.CZ ** p,
-        lambda p: cirq.X ** p,
-        lambda p: cirq.Y ** p,
-        lambda p: cirq.Z ** p,
-        lambda p: cirq.CNOT ** p,
+        lambda p: cirq.CZ**p,
+        lambda p: cirq.X**p,
+        lambda p: cirq.Y**p,
+        lambda p: cirq.Z**p,
+        lambda p: cirq.CNOT**p,
     ]
     for gate in gates:
         eq.add_equality_group(gate(3.5), gate(-0.5))
@@ -250,22 +250,22 @@ def test_rot_gates_eq():
 
 def test_z_unitary():
     assert np.allclose(cirq.unitary(cirq.Z), np.array([[1, 0], [0, -1]]))
-    assert np.allclose(cirq.unitary(cirq.Z ** 0.5), np.array([[1, 0], [0, 1j]]))
-    assert np.allclose(cirq.unitary(cirq.Z ** 0), np.array([[1, 0], [0, 1]]))
-    assert np.allclose(cirq.unitary(cirq.Z ** -0.5), np.array([[1, 0], [0, -1j]]))
+    assert np.allclose(cirq.unitary(cirq.Z**0.5), np.array([[1, 0], [0, 1j]]))
+    assert np.allclose(cirq.unitary(cirq.Z**0), np.array([[1, 0], [0, 1]]))
+    assert np.allclose(cirq.unitary(cirq.Z**-0.5), np.array([[1, 0], [0, -1j]]))
 
 
 def test_y_unitary():
     assert np.allclose(cirq.unitary(cirq.Y), np.array([[0, -1j], [1j, 0]]))
 
     assert np.allclose(
-        cirq.unitary(cirq.Y ** 0.5), np.array([[1 + 1j, -1 - 1j], [1 + 1j, 1 + 1j]]) / 2
+        cirq.unitary(cirq.Y**0.5), np.array([[1 + 1j, -1 - 1j], [1 + 1j, 1 + 1j]]) / 2
     )
 
-    assert np.allclose(cirq.unitary(cirq.Y ** 0), np.array([[1, 0], [0, 1]]))
+    assert np.allclose(cirq.unitary(cirq.Y**0), np.array([[1, 0], [0, 1]]))
 
     assert np.allclose(
-        cirq.unitary(cirq.Y ** -0.5), np.array([[1 - 1j, 1 - 1j], [-1 + 1j, 1 - 1j]]) / 2
+        cirq.unitary(cirq.Y**-0.5), np.array([[1 - 1j, 1 - 1j], [-1 + 1j, 1 - 1j]]) / 2
     )
 
 
@@ -273,18 +273,18 @@ def test_x_unitary():
     assert np.allclose(cirq.unitary(cirq.X), np.array([[0, 1], [1, 0]]))
 
     assert np.allclose(
-        cirq.unitary(cirq.X ** 0.5), np.array([[1 + 1j, 1 - 1j], [1 - 1j, 1 + 1j]]) / 2
+        cirq.unitary(cirq.X**0.5), np.array([[1 + 1j, 1 - 1j], [1 - 1j, 1 + 1j]]) / 2
     )
 
-    assert np.allclose(cirq.unitary(cirq.X ** 0), np.array([[1, 0], [0, 1]]))
+    assert np.allclose(cirq.unitary(cirq.X**0), np.array([[1, 0], [0, 1]]))
 
     assert np.allclose(
-        cirq.unitary(cirq.X ** -0.5), np.array([[1 - 1j, 1 + 1j], [1 + 1j, 1 - 1j]]) / 2
+        cirq.unitary(cirq.X**-0.5), np.array([[1 - 1j, 1 + 1j], [1 + 1j, 1 - 1j]]) / 2
     )
 
 
 def test_h_unitary():
-    sqrt = cirq.unitary(cirq.H ** 0.5)
+    sqrt = cirq.unitary(cirq.H**0.5)
     m = np.dot(sqrt, sqrt)
     assert np.allclose(m, cirq.unitary(cirq.H), atol=1e-8)
 
@@ -296,7 +296,7 @@ def test_h_init():
 
 def test_h_str():
     assert str(cirq.H) == 'H'
-    assert str(cirq.H ** 0.5) == 'H**0.5'
+    assert str(cirq.H**0.5) == 'H**0.5'
 
 
 def test_x_act_on_tableau():
@@ -311,8 +311,8 @@ def test_x_act_on_tableau():
         prng=np.random.RandomState(),
     )
 
-    cirq.act_on(cirq.X ** 0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
-    cirq.act_on(cirq.X ** 0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.X**0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.X**0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
     assert args.log_of_measurement_results == {}
     assert args.tableau == flipped_tableau
 
@@ -320,18 +320,18 @@ def test_x_act_on_tableau():
     assert args.log_of_measurement_results == {}
     assert args.tableau == original_tableau
 
-    cirq.act_on(cirq.X ** 3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
-    cirq.act_on(cirq.X ** 3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.X**3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.X**3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
     assert args.log_of_measurement_results == {}
     assert args.tableau == flipped_tableau
 
-    cirq.act_on(cirq.X ** 2, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.X**2, args, [cirq.LineQubit(1)], allow_decompose=False)
     assert args.log_of_measurement_results == {}
     assert args.tableau == flipped_tableau
 
     foo = sympy.Symbol('foo')
     with pytest.raises(TypeError, match="Failed to act action on state"):
-        cirq.act_on(cirq.X ** foo, args, [cirq.LineQubit(1)])
+        cirq.act_on(cirq.X**foo, args, [cirq.LineQubit(1)])
 
 
 class iZGate(cirq.SingleQubitGate):
@@ -360,8 +360,8 @@ def test_y_act_on_tableau():
         prng=np.random.RandomState(),
     )
 
-    cirq.act_on(cirq.Y ** 0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
-    cirq.act_on(cirq.Y ** 0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.Y**0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.Y**0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
     cirq.act_on(iZGate(), args, [cirq.LineQubit(1)])
     assert args.log_of_measurement_results == {}
     assert args.tableau == flipped_tableau
@@ -371,19 +371,19 @@ def test_y_act_on_tableau():
     assert args.log_of_measurement_results == {}
     assert args.tableau == original_tableau
 
-    cirq.act_on(cirq.Y ** 3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
-    cirq.act_on(cirq.Y ** 3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.Y**3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.Y**3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
     cirq.act_on(iZGate(), args, [cirq.LineQubit(1)])
     assert args.log_of_measurement_results == {}
     assert args.tableau == flipped_tableau
 
-    cirq.act_on(cirq.Y ** 2, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.Y**2, args, [cirq.LineQubit(1)], allow_decompose=False)
     assert args.log_of_measurement_results == {}
     assert args.tableau == flipped_tableau
 
     foo = sympy.Symbol('foo')
     with pytest.raises(TypeError, match="Failed to act action on state"):
-        cirq.act_on(cirq.Y ** foo, args, [cirq.LineQubit(1)])
+        cirq.act_on(cirq.Y**foo, args, [cirq.LineQubit(1)])
 
 
 def test_z_h_act_on_tableau():
@@ -401,8 +401,8 @@ def test_z_h_act_on_tableau():
     )
 
     cirq.act_on(cirq.H, args, [cirq.LineQubit(1)], allow_decompose=False)
-    cirq.act_on(cirq.Z ** 0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
-    cirq.act_on(cirq.Z ** 0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.Z**0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.Z**0.5, args, [cirq.LineQubit(1)], allow_decompose=False)
     cirq.act_on(cirq.H, args, [cirq.LineQubit(1)], allow_decompose=False)
     assert args.log_of_measurement_results == {}
     assert args.tableau == flipped_tableau
@@ -414,29 +414,29 @@ def test_z_h_act_on_tableau():
     assert args.tableau == original_tableau
 
     cirq.act_on(cirq.H, args, [cirq.LineQubit(1)], allow_decompose=False)
-    cirq.act_on(cirq.Z ** 3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
-    cirq.act_on(cirq.Z ** 3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.Z**3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.Z**3.5, args, [cirq.LineQubit(1)], allow_decompose=False)
     cirq.act_on(cirq.H, args, [cirq.LineQubit(1)], allow_decompose=False)
     assert args.log_of_measurement_results == {}
     assert args.tableau == flipped_tableau
 
-    cirq.act_on(cirq.Z ** 2, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.Z**2, args, [cirq.LineQubit(1)], allow_decompose=False)
     assert args.log_of_measurement_results == {}
     assert args.tableau == flipped_tableau
 
-    cirq.act_on(cirq.H ** 2, args, [cirq.LineQubit(1)], allow_decompose=False)
+    cirq.act_on(cirq.H**2, args, [cirq.LineQubit(1)], allow_decompose=False)
     assert args.log_of_measurement_results == {}
     assert args.tableau == flipped_tableau
 
     foo = sympy.Symbol('foo')
     with pytest.raises(TypeError, match="Failed to act action on state"):
-        cirq.act_on(cirq.Z ** foo, args, [cirq.LineQubit(1)])
+        cirq.act_on(cirq.Z**foo, args, [cirq.LineQubit(1)])
 
     with pytest.raises(TypeError, match="Failed to act action on state"):
-        cirq.act_on(cirq.H ** foo, args, [cirq.LineQubit(1)])
+        cirq.act_on(cirq.H**foo, args, [cirq.LineQubit(1)])
 
     with pytest.raises(TypeError, match="Failed to act action on state"):
-        cirq.act_on(cirq.H ** 1.5, args, [cirq.LineQubit(1)])
+        cirq.act_on(cirq.H**1.5, args, [cirq.LineQubit(1)])
 
 
 def test_cx_act_on_tableau():
@@ -471,16 +471,16 @@ def test_cx_act_on_tableau():
     assert args.log_of_measurement_results == {}
     assert args.tableau == original_tableau
 
-    cirq.act_on(cirq.CX ** 4, args, cirq.LineQubit.range(2), allow_decompose=False)
+    cirq.act_on(cirq.CX**4, args, cirq.LineQubit.range(2), allow_decompose=False)
     assert args.log_of_measurement_results == {}
     assert args.tableau == original_tableau
 
     foo = sympy.Symbol('foo')
     with pytest.raises(TypeError, match="Failed to act action on state"):
-        cirq.act_on(cirq.CX ** foo, args, cirq.LineQubit.range(2))
+        cirq.act_on(cirq.CX**foo, args, cirq.LineQubit.range(2))
 
     with pytest.raises(TypeError, match="Failed to act action on state"):
-        cirq.act_on(cirq.CX ** 1.5, args, cirq.LineQubit.range(2))
+        cirq.act_on(cirq.CX**1.5, args, cirq.LineQubit.range(2))
 
 
 def test_cz_act_on_tableau():
@@ -515,16 +515,16 @@ def test_cz_act_on_tableau():
     assert args.log_of_measurement_results == {}
     assert args.tableau == original_tableau
 
-    cirq.act_on(cirq.CZ ** 4, args, cirq.LineQubit.range(2), allow_decompose=False)
+    cirq.act_on(cirq.CZ**4, args, cirq.LineQubit.range(2), allow_decompose=False)
     assert args.log_of_measurement_results == {}
     assert args.tableau == original_tableau
 
     foo = sympy.Symbol('foo')
     with pytest.raises(TypeError, match="Failed to act action on state"):
-        cirq.act_on(cirq.CZ ** foo, args, cirq.LineQubit.range(2))
+        cirq.act_on(cirq.CZ**foo, args, cirq.LineQubit.range(2))
 
     with pytest.raises(TypeError, match="Failed to act action on state"):
-        cirq.act_on(cirq.CZ ** 1.5, args, cirq.LineQubit.range(2))
+        cirq.act_on(cirq.CZ**1.5, args, cirq.LineQubit.range(2))
 
 
 def test_cz_act_on_equivalent_to_h_cx_h_tableau():
@@ -557,33 +557,33 @@ def test_cz_act_on_equivalent_to_h_cx_h_tableau():
 @pytest.mark.parametrize(
     'input_gate_sequence, outcome',
     [
-        ([cirq.X ** foo], 'Error'),
-        ([cirq.X ** 0.25], 'Error'),
-        ([cirq.X ** 4], 'Original'),
-        ([cirq.X ** 0.5, cirq.X ** 0.5], 'Flipped'),
+        ([cirq.X**foo], 'Error'),
+        ([cirq.X**0.25], 'Error'),
+        ([cirq.X**4], 'Original'),
+        ([cirq.X**0.5, cirq.X**0.5], 'Flipped'),
         ([cirq.X], 'Flipped'),
-        ([cirq.X ** 3.5, cirq.X ** 3.5], 'Flipped'),
-        ([cirq.Y ** foo], 'Error'),
-        ([cirq.Y ** 0.25], 'Error'),
-        ([cirq.Y ** 4], 'Original'),
-        ([cirq.Y ** 0.5, cirq.Y ** 0.5, iZGate()], 'Flipped'),
+        ([cirq.X**3.5, cirq.X**3.5], 'Flipped'),
+        ([cirq.Y**foo], 'Error'),
+        ([cirq.Y**0.25], 'Error'),
+        ([cirq.Y**4], 'Original'),
+        ([cirq.Y**0.5, cirq.Y**0.5, iZGate()], 'Flipped'),
         ([cirq.Y, iZGate()], 'Flipped'),
-        ([cirq.Y ** 3.5, cirq.Y ** 3.5, iZGate()], 'Flipped'),
-        ([cirq.Z ** foo], 'Error'),
-        ([cirq.H ** foo], 'Error'),
-        ([cirq.H ** 1.5], 'Error'),
-        ([cirq.Z ** 4], 'Original'),
-        ([cirq.H ** 4], 'Original'),
+        ([cirq.Y**3.5, cirq.Y**3.5, iZGate()], 'Flipped'),
+        ([cirq.Z**foo], 'Error'),
+        ([cirq.H**foo], 'Error'),
+        ([cirq.H**1.5], 'Error'),
+        ([cirq.Z**4], 'Original'),
+        ([cirq.H**4], 'Original'),
         ([cirq.H, cirq.S, cirq.S, cirq.H], 'Flipped'),
         ([cirq.H, cirq.Z, cirq.H], 'Flipped'),
-        ([cirq.H, cirq.Z ** 3.5, cirq.Z ** 3.5, cirq.H], 'Flipped'),
-        ([cirq.CX ** foo], 'Error'),
-        ([cirq.CX ** 1.5], 'Error'),
-        ([cirq.CX ** 4], 'Original'),
+        ([cirq.H, cirq.Z**3.5, cirq.Z**3.5, cirq.H], 'Flipped'),
+        ([cirq.CX**foo], 'Error'),
+        ([cirq.CX**1.5], 'Error'),
+        ([cirq.CX**4], 'Original'),
         ([cirq.CX], 'Flipped'),
-        ([cirq.CZ ** foo], 'Error'),
-        ([cirq.CZ ** 1.5], 'Error'),
-        ([cirq.CZ ** 4], 'Original'),
+        ([cirq.CZ**foo], 'Error'),
+        ([cirq.CZ**1.5], 'Error'),
+        ([cirq.CZ**4], 'Original'),
         ([cirq.CZ, MinusOnePhaseGate()], 'Original'),
     ],
 )
@@ -625,28 +625,28 @@ def test_act_on_ch_form(input_gate_sequence, outcome):
         (cirq.X, True),
         (cirq.Y, True),
         (cirq.Z, True),
-        (cirq.X ** 0.5, True),
-        (cirq.Y ** 0.5, True),
-        (cirq.Z ** 0.5, True),
-        (cirq.X ** 3.5, True),
-        (cirq.Y ** 3.5, True),
-        (cirq.Z ** 3.5, True),
-        (cirq.X ** 4, True),
-        (cirq.Y ** 4, True),
-        (cirq.Z ** 4, True),
+        (cirq.X**0.5, True),
+        (cirq.Y**0.5, True),
+        (cirq.Z**0.5, True),
+        (cirq.X**3.5, True),
+        (cirq.Y**3.5, True),
+        (cirq.Z**3.5, True),
+        (cirq.X**4, True),
+        (cirq.Y**4, True),
+        (cirq.Z**4, True),
         (cirq.H, True),
         (cirq.CX, True),
         (cirq.CZ, True),
-        (cirq.H ** 4, True),
-        (cirq.CX ** 4, True),
-        (cirq.CZ ** 4, True),
+        (cirq.H**4, True),
+        (cirq.CX**4, True),
+        (cirq.CZ**4, True),
         # Unsupported gates should not fail too.
-        (cirq.X ** 0.25, False),
-        (cirq.Y ** 0.25, False),
-        (cirq.Z ** 0.25, False),
-        (cirq.H ** 0.5, False),
-        (cirq.CX ** 0.5, False),
-        (cirq.CZ ** 0.5, False),
+        (cirq.X**0.25, False),
+        (cirq.Y**0.25, False),
+        (cirq.Z**0.25, False),
+        (cirq.H**0.5, False),
+        (cirq.CX**0.5, False),
+        (cirq.CZ**0.5, False),
     ],
 )
 def test_act_on_consistency(input_gate, assert_implemented):
@@ -742,7 +742,7 @@ def test_text_diagrams():
 
 def test_cnot_unitary():
     np.testing.assert_almost_equal(
-        cirq.unitary(cirq.CNOT ** 0.5),
+        cirq.unitary(cirq.CNOT**0.5),
         np.array(
             [
                 [1, 0, 0, 0],
@@ -803,23 +803,23 @@ def test_cnot_decompose():
 
 def test_repr():
     assert repr(cirq.X) == 'cirq.X'
-    assert repr(cirq.X ** 0.5) == '(cirq.X**0.5)'
+    assert repr(cirq.X**0.5) == '(cirq.X**0.5)'
 
     assert repr(cirq.Z) == 'cirq.Z'
-    assert repr(cirq.Z ** 0.5) == 'cirq.S'
-    assert repr(cirq.Z ** 0.25) == 'cirq.T'
-    assert repr(cirq.Z ** 0.125) == '(cirq.Z**0.125)'
+    assert repr(cirq.Z**0.5) == 'cirq.S'
+    assert repr(cirq.Z**0.25) == 'cirq.T'
+    assert repr(cirq.Z**0.125) == '(cirq.Z**0.125)'
 
     assert repr(cirq.S) == 'cirq.S'
-    assert repr(cirq.S ** -1) == '(cirq.S**-1)'
+    assert repr(cirq.S**-1) == '(cirq.S**-1)'
     assert repr(cirq.T) == 'cirq.T'
-    assert repr(cirq.T ** -1) == '(cirq.T**-1)'
+    assert repr(cirq.T**-1) == '(cirq.T**-1)'
 
     assert repr(cirq.Y) == 'cirq.Y'
-    assert repr(cirq.Y ** 0.5) == '(cirq.Y**0.5)'
+    assert repr(cirq.Y**0.5) == '(cirq.Y**0.5)'
 
     assert repr(cirq.CNOT) == 'cirq.CNOT'
-    assert repr(cirq.CNOT ** 0.5) == '(cirq.CNOT**0.5)'
+    assert repr(cirq.CNOT**0.5) == '(cirq.CNOT**0.5)'
 
     cirq.testing.assert_equivalent_repr(
         cirq.X ** (sympy.Symbol('a') / 2 - sympy.Symbol('c') * 3 + 5)
@@ -832,30 +832,30 @@ def test_repr():
     # should be using the "shortest decimal value closer to X than any other
     # floating point value" strategy, as opposed to the "exactly value in
     # decimal" strategy.
-    assert repr(cirq.CZ ** 0.2) == '(cirq.CZ**0.2)'
+    assert repr(cirq.CZ**0.2) == '(cirq.CZ**0.2)'
 
 
 def test_str():
     assert str(cirq.X) == 'X'
-    assert str(cirq.X ** 0.5) == 'X**0.5'
+    assert str(cirq.X**0.5) == 'X**0.5'
     assert str(cirq.rx(np.pi)) == 'Rx(π)'
     assert str(cirq.rx(0.5 * np.pi)) == 'Rx(0.5π)'
     assert str(cirq.XPowGate(global_shift=-0.25)) == 'XPowGate(exponent=1.0, global_shift=-0.25)'
 
     assert str(cirq.Z) == 'Z'
-    assert str(cirq.Z ** 0.5) == 'S'
-    assert str(cirq.Z ** 0.125) == 'Z**0.125'
+    assert str(cirq.Z**0.5) == 'S'
+    assert str(cirq.Z**0.125) == 'Z**0.125'
     assert str(cirq.rz(np.pi)) == 'Rz(π)'
     assert str(cirq.rz(1.4 * np.pi)) == 'Rz(1.4π)'
     assert str(cirq.ZPowGate(global_shift=0.25)) == 'ZPowGate(exponent=1.0, global_shift=0.25)'
 
     assert str(cirq.S) == 'S'
-    assert str(cirq.S ** -1) == 'S**-1'
+    assert str(cirq.S**-1) == 'S**-1'
     assert str(cirq.T) == 'T'
-    assert str(cirq.T ** -1) == 'T**-1'
+    assert str(cirq.T**-1) == 'T**-1'
 
     assert str(cirq.Y) == 'Y'
-    assert str(cirq.Y ** 0.5) == 'Y**0.5'
+    assert str(cirq.Y**0.5) == 'Y**0.5'
     assert str(cirq.ry(np.pi)) == 'Ry(π)'
     assert str(cirq.ry(3.14 * np.pi)) == 'Ry(3.14π)'
     assert (
@@ -864,9 +864,9 @@ def test_str():
     )
 
     assert str(cirq.CX) == 'CNOT'
-    assert str(cirq.CNOT ** 0.5) == 'CNOT**0.5'
+    assert str(cirq.CNOT**0.5) == 'CNOT**0.5'
     assert str(cirq.CZ) == 'CZ'
-    assert str(cirq.CZ ** 0.5) == 'CZ**0.5'
+    assert str(cirq.CZ**0.5) == 'CZ**0.5'
     assert str(cirq.cphase(np.pi)) == 'CZ'
     assert str(cirq.cphase(np.pi / 2)) == 'CZ**0.5'
 
@@ -938,49 +938,49 @@ def test_cphase_unitary(angle_rads, expected_unitary):
 
 def test_parameterized_cphase():
     assert cirq.cphase(sympy.pi) == cirq.CZ
-    assert cirq.cphase(sympy.pi / 2) == cirq.CZ ** 0.5
+    assert cirq.cphase(sympy.pi / 2) == cirq.CZ**0.5
 
 
 @pytest.mark.parametrize('gate', [cirq.X, cirq.Y, cirq.Z])
 def test_x_y_z_stabilizer(gate):
     assert cirq.has_stabilizer_effect(gate)
-    assert cirq.has_stabilizer_effect(gate ** 0.5)
-    assert cirq.has_stabilizer_effect(gate ** 0)
-    assert cirq.has_stabilizer_effect(gate ** -0.5)
-    assert cirq.has_stabilizer_effect(gate ** 4)
-    assert not cirq.has_stabilizer_effect(gate ** 1.2)
+    assert cirq.has_stabilizer_effect(gate**0.5)
+    assert cirq.has_stabilizer_effect(gate**0)
+    assert cirq.has_stabilizer_effect(gate**-0.5)
+    assert cirq.has_stabilizer_effect(gate**4)
+    assert not cirq.has_stabilizer_effect(gate**1.2)
     foo = sympy.Symbol('foo')
-    assert not cirq.has_stabilizer_effect(gate ** foo)
+    assert not cirq.has_stabilizer_effect(gate**foo)
 
 
 def test_h_stabilizer():
     gate = cirq.H
     assert cirq.has_stabilizer_effect(gate)
-    assert not cirq.has_stabilizer_effect(gate ** 0.5)
-    assert cirq.has_stabilizer_effect(gate ** 0)
-    assert not cirq.has_stabilizer_effect(gate ** -0.5)
-    assert cirq.has_stabilizer_effect(gate ** 4)
-    assert not cirq.has_stabilizer_effect(gate ** 1.2)
+    assert not cirq.has_stabilizer_effect(gate**0.5)
+    assert cirq.has_stabilizer_effect(gate**0)
+    assert not cirq.has_stabilizer_effect(gate**-0.5)
+    assert cirq.has_stabilizer_effect(gate**4)
+    assert not cirq.has_stabilizer_effect(gate**1.2)
     foo = sympy.Symbol('foo')
-    assert not cirq.has_stabilizer_effect(gate ** foo)
+    assert not cirq.has_stabilizer_effect(gate**foo)
 
 
 @pytest.mark.parametrize('gate', [cirq.CX, cirq.CZ])
 def test_cx_cz_stabilizer(gate):
     assert cirq.has_stabilizer_effect(gate)
-    assert not cirq.has_stabilizer_effect(gate ** 0.5)
-    assert cirq.has_stabilizer_effect(gate ** 0)
-    assert not cirq.has_stabilizer_effect(gate ** -0.5)
-    assert cirq.has_stabilizer_effect(gate ** 4)
-    assert not cirq.has_stabilizer_effect(gate ** 1.2)
+    assert not cirq.has_stabilizer_effect(gate**0.5)
+    assert cirq.has_stabilizer_effect(gate**0)
+    assert not cirq.has_stabilizer_effect(gate**-0.5)
+    assert cirq.has_stabilizer_effect(gate**4)
+    assert not cirq.has_stabilizer_effect(gate**1.2)
     foo = sympy.Symbol('foo')
-    assert not cirq.has_stabilizer_effect(gate ** foo)
+    assert not cirq.has_stabilizer_effect(gate**foo)
 
 
 def test_phase_by_xy():
     assert cirq.phase_by(cirq.X, 0.25, 0) == cirq.Y
-    assert cirq.phase_by(cirq.X ** 0.5, 0.25, 0) == cirq.Y ** 0.5
-    assert cirq.phase_by(cirq.X ** -0.5, 0.25, 0) == cirq.Y ** -0.5
+    assert cirq.phase_by(cirq.X**0.5, 0.25, 0) == cirq.Y**0.5
+    assert cirq.phase_by(cirq.X**-0.5, 0.25, 0) == cirq.Y**-0.5
 
 
 def test_ixyz_circuit_diagram():
@@ -1108,12 +1108,12 @@ def test_rxyz_circuit_diagram():
 
 def test_trace_distance():
     foo = sympy.Symbol('foo')
-    sx = cirq.X ** foo
-    sy = cirq.Y ** foo
-    sz = cirq.Z ** foo
-    sh = cirq.H ** foo
-    scx = cirq.CX ** foo
-    scz = cirq.CZ ** foo
+    sx = cirq.X**foo
+    sy = cirq.Y**foo
+    sz = cirq.Z**foo
+    sh = cirq.H**foo
+    scx = cirq.CX**foo
+    scz = cirq.CZ**foo
     # These values should have 1.0 or 0.0 directly returned
     assert cirq.trace_distance_bound(sx) == 1.0
     assert cirq.trace_distance_bound(sy) == 1.0
@@ -1124,23 +1124,23 @@ def test_trace_distance():
     assert cirq.trace_distance_bound(cirq.I) == 0.0
     # These values are calculated, so we use approx_eq
     assert cirq.approx_eq(cirq.trace_distance_bound(cirq.X), 1.0)
-    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.Y ** -1), 1.0)
-    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.Z ** 0.5), np.sin(np.pi / 4))
-    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.H ** 0.25), np.sin(np.pi / 8))
-    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.CX ** 2), 0.0)
+    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.Y**-1), 1.0)
+    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.Z**0.5), np.sin(np.pi / 4))
+    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.H**0.25), np.sin(np.pi / 8))
+    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.CX**2), 0.0)
     assert cirq.approx_eq(cirq.trace_distance_bound(cirq.CZ ** (1 / 9)), np.sin(np.pi / 18))
 
 
 def test_commutes():
     assert cirq.commutes(cirq.ZPowGate(exponent=sympy.Symbol('t')), cirq.Z)
     assert cirq.commutes(cirq.Z, cirq.Z(cirq.LineQubit(0)), default=None) is None
-    assert cirq.commutes(cirq.Z ** 0.1, cirq.XPowGate(exponent=0))
+    assert cirq.commutes(cirq.Z**0.1, cirq.XPowGate(exponent=0))
 
 
 def test_approx_eq():
-    assert cirq.approx_eq(cirq.Z ** 0.1, cirq.Z ** 0.2, atol=0.3)
-    assert not cirq.approx_eq(cirq.Z ** 0.1, cirq.Z ** 0.2, atol=0.05)
-    assert cirq.approx_eq(cirq.Y ** 0.1, cirq.Y ** 0.2, atol=0.3)
-    assert not cirq.approx_eq(cirq.Y ** 0.1, cirq.Y ** 0.2, atol=0.05)
-    assert cirq.approx_eq(cirq.X ** 0.1, cirq.X ** 0.2, atol=0.3)
-    assert not cirq.approx_eq(cirq.X ** 0.1, cirq.X ** 0.2, atol=0.05)
+    assert cirq.approx_eq(cirq.Z**0.1, cirq.Z**0.2, atol=0.3)
+    assert not cirq.approx_eq(cirq.Z**0.1, cirq.Z**0.2, atol=0.05)
+    assert cirq.approx_eq(cirq.Y**0.1, cirq.Y**0.2, atol=0.3)
+    assert not cirq.approx_eq(cirq.Y**0.1, cirq.Y**0.2, atol=0.05)
+    assert cirq.approx_eq(cirq.X**0.1, cirq.X**0.2, atol=0.3)
+    assert not cirq.approx_eq(cirq.X**0.1, cirq.X**0.2, atol=0.05)
diff --git a/cirq/ops/controlled_gate_test.py b/cirq/ops/controlled_gate_test.py
index 67495a5f47a..1b570938524 100644
--- a/cirq/ops/controlled_gate_test.py
+++ b/cirq/ops/controlled_gate_test.py
@@ -328,7 +328,7 @@ def test_unitary():
     'gate, should_decompose_to_target',
     [
         (cirq.X, True),
-        (cirq.X ** 0.5, True),
+        (cirq.X**0.5, True),
         (cirq.rx(np.pi), True),
         (cirq.rx(np.pi / 2), True),
         (cirq.Z, True),
@@ -366,45 +366,45 @@ def test_controlled_gate_is_consistent(gate: cirq.Gate, should_decompose_to_targ
 def test_pow_inverse():
     assert cirq.inverse(CRestricted, None) is None
     assert cirq.pow(CRestricted, 1.5, None) is None
-    assert cirq.pow(CY, 1.5) == cirq.ControlledGate(cirq.Y ** 1.5)
-    assert cirq.inverse(CY) == CY ** -1 == CY
+    assert cirq.pow(CY, 1.5) == cirq.ControlledGate(cirq.Y**1.5)
+    assert cirq.inverse(CY) == CY**-1 == CY
 
     assert cirq.inverse(C0Restricted, None) is None
     assert cirq.pow(C0Restricted, 1.5, None) is None
-    assert cirq.pow(C0Y, 1.5) == cirq.ControlledGate(cirq.Y ** 1.5, control_values=[0])
-    assert cirq.inverse(C0Y) == C0Y ** -1 == C0Y
+    assert cirq.pow(C0Y, 1.5) == cirq.ControlledGate(cirq.Y**1.5, control_values=[0])
+    assert cirq.inverse(C0Y) == C0Y**-1 == C0Y
 
     assert cirq.inverse(C2Restricted, None) is None
     assert cirq.pow(C2Restricted, 1.5, None) is None
     assert cirq.pow(C2Y, 1.5) == cirq.ControlledGate(
-        cirq.Y ** 1.5, control_values=[2], control_qid_shape=(3,)
+        cirq.Y**1.5, control_values=[2], control_qid_shape=(3,)
     )
-    assert cirq.inverse(C2Y) == C2Y ** -1 == C2Y
+    assert cirq.inverse(C2Y) == C2Y**-1 == C2Y
 
 
 def test_extrapolatable_effect():
     a = cirq.NamedQubit('a')
     b = cirq.NamedQubit('b')
 
-    assert cirq.ControlledGate(cirq.Z) ** 0.5 == cirq.ControlledGate(cirq.Z ** 0.5)
+    assert cirq.ControlledGate(cirq.Z) ** 0.5 == cirq.ControlledGate(cirq.Z**0.5)
 
-    assert cirq.ControlledGate(cirq.Z).on(a, b) ** 0.5 == cirq.ControlledGate(cirq.Z ** 0.5).on(
+    assert cirq.ControlledGate(cirq.Z).on(a, b) ** 0.5 == cirq.ControlledGate(cirq.Z**0.5).on(
         a, b
     )
 
-    assert cirq.ControlledGate(cirq.Z) ** 0.5 == cirq.ControlledGate(cirq.Z ** 0.5)
+    assert cirq.ControlledGate(cirq.Z) ** 0.5 == cirq.ControlledGate(cirq.Z**0.5)
 
 
 def test_reversible():
-    assert cirq.inverse(cirq.ControlledGate(cirq.S)) == cirq.ControlledGate(cirq.S ** -1)
+    assert cirq.inverse(cirq.ControlledGate(cirq.S)) == cirq.ControlledGate(cirq.S**-1)
     assert cirq.inverse(cirq.ControlledGate(cirq.S, num_controls=4)) == cirq.ControlledGate(
-        cirq.S ** -1, num_controls=4
+        cirq.S**-1, num_controls=4
     )
     assert cirq.inverse(cirq.ControlledGate(cirq.S, control_values=[1])) == cirq.ControlledGate(
-        cirq.S ** -1, control_values=[1]
+        cirq.S**-1, control_values=[1]
     )
     assert cirq.inverse(cirq.ControlledGate(cirq.S, control_qid_shape=(3,))) == cirq.ControlledGate(
-        cirq.S ** -1, control_qid_shape=(3,)
+        cirq.S**-1, control_qid_shape=(3,)
     )
 
 
@@ -435,7 +435,7 @@ def test_circuit_diagram_info():
         wire_symbols=('(2)', 'Y'), exponent=1
     )
 
-    assert cirq.circuit_diagram_info(cirq.ControlledGate(cirq.Y ** 0.5)) == cirq.CircuitDiagramInfo(
+    assert cirq.circuit_diagram_info(cirq.ControlledGate(cirq.Y**0.5)) == cirq.CircuitDiagramInfo(
         wire_symbols=('@', 'Y'), exponent=0.5
     )
 
@@ -525,11 +525,11 @@ def test_uninformed_circuit_diagram_info():
 
 
 def test_bounded_effect():
-    assert cirq.trace_distance_bound(CY ** 0.001) < 0.01
+    assert cirq.trace_distance_bound(CY**0.001) < 0.01
     assert cirq.approx_eq(cirq.trace_distance_bound(CCH), 1.0)
     assert cirq.approx_eq(cirq.trace_distance_bound(CRestricted), 1.0)
     foo = sympy.Symbol('foo')
-    assert cirq.trace_distance_bound(cirq.ControlledGate(cirq.X ** foo)) == 1
+    assert cirq.trace_distance_bound(cirq.ControlledGate(cirq.X**foo)) == 1
 
 
 def test_repr():
@@ -544,7 +544,7 @@ def test_str():
     assert str(cirq.ControlledGate(cirq.X)) == 'CX'
     assert str(cirq.ControlledGate(cirq.Z)) == 'CZ'
     assert str(cirq.ControlledGate(cirq.S)) == 'CS'
-    assert str(cirq.ControlledGate(cirq.Z ** 0.125)) == 'CZ**0.125'
+    assert str(cirq.ControlledGate(cirq.Z**0.125)) == 'CZ**0.125'
     assert str(cirq.ControlledGate(cirq.ControlledGate(cirq.S))) == 'CCS'
     assert str(C0Y) == 'C0Y'
     assert str(C0C1H) == 'C0C1H'
diff --git a/cirq/ops/controlled_operation_test.py b/cirq/ops/controlled_operation_test.py
index 18198871cab..333b7077108 100644
--- a/cirq/ops/controlled_operation_test.py
+++ b/cirq/ops/controlled_operation_test.py
@@ -399,7 +399,7 @@ def test_parameterizable(resolve_fn):
 def test_bounded_effect():
     qubits = cirq.LineQubit.range(3)
     cy = cirq.ControlledOperation(qubits[:1], cirq.Y(qubits[1]))
-    assert cirq.trace_distance_bound(cy ** 0.001) < 0.01
+    assert cirq.trace_distance_bound(cy**0.001) < 0.01
     foo = sympy.Symbol('foo')
     scy = cirq.ControlledOperation(qubits[:1], cirq.Y(qubits[1]) ** foo)
     assert cirq.trace_distance_bound(scy) == 1.0
diff --git a/cirq/ops/dense_pauli_string.py b/cirq/ops/dense_pauli_string.py
index 1aa67bc4e36..143b9e13f61 100644
--- a/cirq/ops/dense_pauli_string.py
+++ b/cirq/ops/dense_pauli_string.py
@@ -211,7 +211,7 @@ def __pow__(self, power):
             if self.coefficient in i_group:
                 coef = i_group[i_group.index(self.coefficient) * power % 4]
             else:
-                coef = self.coefficient ** power
+                coef = self.coefficient**power
             if power % 2 == 0:
                 return coef * DensePauliString.eye(len(self))
             return DensePauliString(coefficient=coef, pauli_mask=self.pauli_mask)
@@ -585,4 +585,4 @@ def _vectorized_pauli_mul_phase(
 
     # Result is i raised to the sum of the per-term phase exponents.
     s = int(np.sum(t, dtype=np.uint8).item() & 3)
-    return 1j ** s
+    return 1j**s
diff --git a/cirq/ops/dense_pauli_string_test.py b/cirq/ops/dense_pauli_string_test.py
index 44951cab48d..848b4a4d130 100644
--- a/cirq/ops/dense_pauli_string_test.py
+++ b/cirq/ops/dense_pauli_string_test.py
@@ -278,33 +278,33 @@ def test_pow():
     f = cirq.DensePauliString
     m = cirq.DensePauliString
     p = 1j * f('IXYZ')
-    assert p ** 0 == p ** 4 == p ** 8 == cirq.DensePauliString.eye(4)
-    assert p ** 1 == p ** 5 == p ** -3 == p == p ** 101
-    assert p ** 2 == p ** -2 == p ** 6 == -f('IIII')
-    assert p ** 3 == p ** -1 == p ** 7 == -1j * f('IXYZ')
+    assert p**0 == p**4 == p**8 == cirq.DensePauliString.eye(4)
+    assert p**1 == p**5 == p**-3 == p == p**101
+    assert p**2 == p**-2 == p**6 == -f('IIII')
+    assert p**3 == p**-1 == p**7 == -1j * f('IXYZ')
 
     p = -f('IXYZ')
-    assert p == p ** 1 == p ** -1 == p ** -3 == p ** -303
-    assert p ** 0 == p ** 2 == p ** -2 == p ** -4 == p ** 102
+    assert p == p**1 == p**-1 == p**-3 == p**-303
+    assert p**0 == p**2 == p**-2 == p**-4 == p**102
 
     p = 2 * f('XX')
-    assert p ** -1 == (0.5 + 0j) * f('XX')
-    assert p ** 0 == f('II')
-    assert p ** 1 == 2 * f('XX')
-    assert p ** 2 == 4 * f('II')
-    assert p ** 3 == 8 * f('XX')
-    assert p ** 4 == 16 * f('II')
+    assert p**-1 == (0.5 + 0j) * f('XX')
+    assert p**0 == f('II')
+    assert p**1 == 2 * f('XX')
+    assert p**2 == 4 * f('II')
+    assert p**3 == 8 * f('XX')
+    assert p**4 == 16 * f('II')
 
     p = -1j * f('XY')
-    assert p ** 101 == p == p ** -103
+    assert p**101 == p == p**-103
 
     p = 2j * f('XY')
-    assert (p ** -1) ** -1 == p
-    assert p ** -2 == f('II') / -4
+    assert (p**-1) ** -1 == p
+    assert p**-2 == f('II') / -4
 
     p = f('XY')
-    assert p ** -100 == p ** 0 == p ** 100 == f('II')
-    assert p ** -101 == p ** 1 == p ** 101 == f('XY')
+    assert p**-100 == p**0 == p**100 == f('II')
+    assert p**-101 == p**1 == p**101 == f('XY')
 
     # Becomes an immutable copy.
     assert m('X') ** 3 == f('X')
diff --git a/cirq/ops/diagonal_gate.py b/cirq/ops/diagonal_gate.py
index 670a683f675..f05c77af9e5 100644
--- a/cirq/ops/diagonal_gate.py
+++ b/cirq/ops/diagonal_gate.py
@@ -54,7 +54,7 @@ def _gen_gray_code(n: int) -> Iterator[Tuple[int, int]]:
     gray code.
     """
     gray_code = 0
-    for i in range(1, 2 ** n):
+    for i in range(1, 2**n):
         next_gray = i ^ (i >> 1)
         bit_flip = int(np.log2(gray_code ^ next_gray))
         yield gray_code, bit_flip
@@ -177,7 +177,7 @@ def _decompose_(self, qubits: Sequence['cirq.Qid']) -> 'cirq.OP_TREE':
             https://iopscience.iop.org/article/10.1088/1367-2630/16/3/033040/meta
         """
         n = self._num_qubits_()
-        hat_angles = _fast_walsh_hadamard_transform(self._diag_angles_radians) / (2 ** n)
+        hat_angles = _fast_walsh_hadamard_transform(self._diag_angles_radians) / (2**n)
 
         # There is one global phase shift between unitary matrix of the diagonal gate and the
         # decomposed gates. On its own it is not physically observable. However, if using this
diff --git a/cirq/ops/diagonal_gate_test.py b/cirq/ops/diagonal_gate_test.py
index c4529766628..21690904b71 100644
--- a/cirq/ops/diagonal_gate_test.py
+++ b/cirq/ops/diagonal_gate_test.py
@@ -41,7 +41,7 @@ def test_consistent_protocols(gate):
 
 @pytest.mark.parametrize('n', [1, 2, 3, 4, 5, 6, 7, 8, 9])
 def test_decomposition_unitary(n):
-    diagonal_angles = np.random.randn(2 ** n)
+    diagonal_angles = np.random.randn(2**n)
     diagonal_gate = cirq.DiagonalGate(diagonal_angles)
     decomposed_circ = cirq.Circuit(cirq.decompose(diagonal_gate(*cirq.LineQubit.range(n))))
 
@@ -53,10 +53,10 @@ def test_decomposition_unitary(n):
 
 @pytest.mark.parametrize('n', [1, 2, 3, 4])
 def test_diagonal_exponent(n):
-    diagonal_angles = _candidate_angles[: 2 ** n]
+    diagonal_angles = _candidate_angles[: 2**n]
     diagonal_gate = cirq.DiagonalGate(diagonal_angles)
 
-    sqrt_diagonal_gate = diagonal_gate ** 0.5
+    sqrt_diagonal_gate = diagonal_gate**0.5
 
     expected_angles = [prime / 2 for prime in diagonal_angles]
     np.testing.assert_allclose(expected_angles, sqrt_diagonal_gate._diag_angles_radians, atol=1e-8)
@@ -66,9 +66,9 @@ def test_diagonal_exponent(n):
 
 @pytest.mark.parametrize('n', [1, 2, 3, 4])
 def test_decomposition_diagonal_exponent(n):
-    diagonal_angles = np.random.randn(2 ** n)
+    diagonal_angles = np.random.randn(2**n)
     diagonal_gate = cirq.DiagonalGate(diagonal_angles)
-    sqrt_diagonal_gate = diagonal_gate ** 0.5
+    sqrt_diagonal_gate = diagonal_gate**0.5
     decomposed_circ = cirq.Circuit(cirq.decompose(sqrt_diagonal_gate(*cirq.LineQubit.range(n))))
 
     expected_f = [np.exp(1j * angle / 2) for angle in diagonal_angles]
@@ -79,16 +79,16 @@ def test_decomposition_diagonal_exponent(n):
 
 @pytest.mark.parametrize('n', [1, 2, 3, 4])
 def test_decomposition_with_parameterization(n):
-    angles = sympy.symbols([f'x_{i}' for i in range(2 ** n)])
+    angles = sympy.symbols([f'x_{i}' for i in range(2**n)])
     exponent = sympy.Symbol('e')
     diagonal_gate = cirq.DiagonalGate(angles) ** exponent
     parameterized_op = diagonal_gate(*cirq.LineQubit.range(n))
     decomposed_circuit = cirq.Circuit(cirq.decompose(parameterized_op))
     for exponent_value in [-0.5, 0.5, 1]:
-        for i in range(len(_candidate_angles) - 2 ** n + 1):
+        for i in range(len(_candidate_angles) - 2**n + 1):
             resolver = {exponent: exponent_value}
             resolver.update(
-                {angles[j]: x_j for j, x_j in enumerate(_candidate_angles[i : i + 2 ** n])}
+                {angles[j]: x_j for j, x_j in enumerate(_candidate_angles[i : i + 2**n])}
             )
             resolved_op = cirq.resolve_parameters(parameterized_op, resolver)
             resolved_circuit = cirq.resolve_parameters(decomposed_circuit, resolver)
@@ -139,7 +139,7 @@ def test_diagram():
 
 @pytest.mark.parametrize('n', [1, 2, 3, 4])
 def test_unitary(n):
-    diagonal_angles = _candidate_angles[: 2 ** n]
+    diagonal_angles = _candidate_angles[: 2**n]
     assert cirq.has_unitary(cirq.DiagonalGate(diagonal_angles))
     np.testing.assert_allclose(
         cirq.unitary(cirq.DiagonalGate(diagonal_angles)).diagonal(),
diff --git a/cirq/ops/eigen_gate_test.py b/cirq/ops/eigen_gate_test.py
index 49d27d19ce1..8e2d64f8614 100644
--- a/cirq/ops/eigen_gate_test.py
+++ b/cirq/ops/eigen_gate_test.py
@@ -356,19 +356,19 @@ def _with_exponent(self, exponent):
 @pytest.mark.parametrize(
     'gate1,gate2,eq_up_to_global_phase',
     [
-        (cirq.rz(0.3 * np.pi), cirq.Z ** 0.3, True),
+        (cirq.rz(0.3 * np.pi), cirq.Z**0.3, True),
         (cirq.Z, cirq.Gate, False),
-        (cirq.rz(0.3), cirq.Z ** 0.3, False),
+        (cirq.rz(0.3), cirq.Z**0.3, False),
         (cirq.ZZPowGate(global_shift=0.5), cirq.ZZ, True),
         (cirq.ZPowGate(global_shift=0.5) ** sympy.Symbol('e'), cirq.Z, False),
         (cirq.Z ** sympy.Symbol('e'), cirq.Z ** sympy.Symbol('f'), False),
-        (cirq.ZZ ** 1.9, cirq.ZZ ** -0.1, True),
+        (cirq.ZZ**1.9, cirq.ZZ**-0.1, True),
         (WeightedZPowGate(0), WeightedZPowGate(0.1), False),
         (WeightedZPowGate(0.3), WeightedZPowGate(0.3, global_shift=0.1), True),
         (cirq.X, cirq.Z, False),
         (cirq.X, cirq.Y, False),
         (cirq.rz(np.pi), cirq.Z, True),
-        (cirq.X ** 0.3, cirq.Z ** 0.3, False),
+        (cirq.X**0.3, cirq.Z**0.3, False),
     ],
 )
 def test_equal_up_to_global_phase(gate1, gate2, eq_up_to_global_phase):
diff --git a/cirq/ops/fourier_transform.py b/cirq/ops/fourier_transform.py
index 35560e698e2..4a19c34a911 100644
--- a/cirq/ops/fourier_transform.py
+++ b/cirq/ops/fourier_transform.py
@@ -122,7 +122,7 @@ def num_qubits(self) -> int:
 
     def _decompose_(self, qubits):
         for i, q in enumerate(qubits):
-            yield cirq.Z(q) ** (self.exponent / 2 ** i)
+            yield cirq.Z(q) ** (self.exponent / 2**i)
 
     def _apply_unitary_(self, args: 'cirq.ApplyUnitaryArgs'):
         if isinstance(self.exponent, sympy.Basic):
diff --git a/cirq/ops/fourier_transform_test.py b/cirq/ops/fourier_transform_test.py
index 57e4d5bf9eb..6b1a474940b 100644
--- a/cirq/ops/fourier_transform_test.py
+++ b/cirq/ops/fourier_transform_test.py
@@ -59,7 +59,7 @@ def test_quantum_fourier_transform_gate_repr():
 
 def test_pow():
     a = cirq.PhaseGradientGate(num_qubits=2, exponent=0.5)
-    assert a ** 0.5 == cirq.PhaseGradientGate(num_qubits=2, exponent=0.25)
+    assert a**0.5 == cirq.PhaseGradientGate(num_qubits=2, exponent=0.25)
     assert a ** sympy.Symbol('t') == cirq.PhaseGradientGate(
         num_qubits=2, exponent=0.5 * sympy.Symbol('t')
     )
diff --git a/cirq/ops/gate_operation_test.py b/cirq/ops/gate_operation_test.py
index 67554537bb5..aeaceadbc29 100644
--- a/cirq/ops/gate_operation_test.py
+++ b/cirq/ops/gate_operation_test.py
@@ -138,7 +138,7 @@ def _num_qubits_(self):
 def test_gate_operation_pow():
     Y = cirq.Y
     q = cirq.NamedQubit('q')
-    assert (Y ** 0.5)(q) == Y(q) ** 0.5
+    assert (Y**0.5)(q) == Y(q) ** 0.5
 
 
 def test_with_qubits_and_transform_qubits():
@@ -159,11 +159,11 @@ def test_extrapolate():
     # If the gate isn't extrapolatable, you get a type error.
     op0 = cirq.GateOperation(cirq.SingleQubitGate(), [q])
     with pytest.raises(TypeError):
-        _ = op0 ** 0.5
+        _ = op0**0.5
 
     op1 = cirq.GateOperation(cirq.Y, [q])
-    assert op1 ** 0.5 == cirq.GateOperation(cirq.Y ** 0.5, [q])
-    assert (cirq.Y ** 0.5).on(q) == cirq.Y(q) ** 0.5
+    assert op1**0.5 == cirq.GateOperation(cirq.Y**0.5, [q])
+    assert (cirq.Y**0.5).on(q) == cirq.Y(q) ** 0.5
 
 
 def test_inverse():
@@ -174,7 +174,7 @@ def test_inverse():
     assert cirq.inverse(op0, None) is None
 
     op1 = cirq.GateOperation(cirq.S, [q])
-    assert cirq.inverse(op1) == op1 ** -1 == cirq.GateOperation(cirq.S ** -1, [q])
+    assert cirq.inverse(op1) == op1**-1 == cirq.GateOperation(cirq.S**-1, [q])
     assert cirq.inverse(cirq.S).on(q) == cirq.inverse(cirq.S.on(q))
 
 
@@ -198,9 +198,9 @@ def test_bounded_effect():
     # If the gate isn't bounded, you get a type error.
     op0 = cirq.GateOperation(cirq.SingleQubitGate(), [q])
     assert cirq.trace_distance_bound(op0) >= 1
-    op1 = cirq.GateOperation(cirq.Z ** 0.000001, [q])
+    op1 = cirq.GateOperation(cirq.Z**0.000001, [q])
     op1_bound = cirq.trace_distance_bound(op1)
-    assert op1_bound == cirq.trace_distance_bound(cirq.Z ** 0.000001)
+    assert op1_bound == cirq.trace_distance_bound(cirq.Z**0.000001)
 
 
 @pytest.mark.parametrize('resolve_fn', [cirq.resolve_parameters, cirq.resolve_parameters_once])
@@ -304,8 +304,8 @@ def on(self, *qubits):
 @pytest.mark.parametrize(
     'gate1,gate2,eq_up_to_global_phase',
     [
-        (cirq.rz(0.3 * np.pi), cirq.Z ** 0.3, True),
-        (cirq.rz(0.3), cirq.Z ** 0.3, False),
+        (cirq.rz(0.3 * np.pi), cirq.Z**0.3, True),
+        (cirq.rz(0.3), cirq.Z**0.3, False),
         (cirq.ZZPowGate(global_shift=0.5), cirq.ZZ, True),
         (cirq.ZPowGate(global_shift=0.5) ** sympy.Symbol('e'), cirq.Z, False),
         (cirq.Z ** sympy.Symbol('e'), cirq.Z ** sympy.Symbol('f'), False),
diff --git a/cirq/ops/gateset_test.py b/cirq/ops/gateset_test.py
index 6c1e1a36224..5bfc0c786d1 100644
--- a/cirq/ops/gateset_test.py
+++ b/cirq/ops/gateset_test.py
@@ -108,10 +108,10 @@ def test_gate_family_json(gate, name, description):
 def test_gate_family_eq():
     eq = cirq.testing.EqualsTester()
     eq.add_equality_group(cirq.GateFamily(CustomX))
-    eq.add_equality_group(cirq.GateFamily(CustomX ** 3))
+    eq.add_equality_group(cirq.GateFamily(CustomX**3))
     eq.add_equality_group(
         cirq.GateFamily(CustomX, name='custom_name', description='custom_description'),
-        cirq.GateFamily(CustomX ** 3, name='custom_name', description='custom_description'),
+        cirq.GateFamily(CustomX**3, name='custom_name', description='custom_description'),
     )
     eq.add_equality_group(cirq.GateFamily(CustomXPowGate))
     eq.add_equality_group(
@@ -126,11 +126,11 @@ def test_gate_family_eq():
             cirq.GateFamily(CustomXPowGate),
             [
                 (CustomX, True),
-                (CustomX ** 0.5, True),
+                (CustomX**0.5, True),
                 (CustomX ** sympy.Symbol('theta'), True),
                 (CustomXPowGate(exponent=0.25, global_shift=0.15), True),
                 (cirq.SingleQubitGate(), False),
-                (cirq.X ** 0.5, False),
+                (cirq.X**0.5, False),
                 (None, False),
                 (cirq.global_phase_operation(1j), False),
             ],
@@ -140,8 +140,8 @@ def test_gate_family_eq():
             [
                 (CustomX, True),
                 (CustomXPowGate(exponent=1, global_shift=0.15), True),
-                (CustomX ** 2, False),
-                (CustomX ** 3, True),
+                (CustomX**2, False),
+                (CustomX**3, True),
                 (CustomX ** sympy.Symbol('theta'), False),
                 (None, False),
                 (cirq.global_phase_operation(1j), False),
@@ -188,7 +188,7 @@ def __repr__(self):
 
 
 gateset = cirq.Gateset(
-    CustomX ** 0.5, cirq.testing.TwoQubitGate, CustomXGateFamily(), name='custom gateset'
+    CustomX**0.5, cirq.testing.TwoQubitGate, CustomXGateFamily(), name='custom gateset'
 )
 
 
@@ -196,7 +196,7 @@ def test_gateset_init():
     assert gateset.name == 'custom gateset'
     assert gateset.gates == frozenset(
         [
-            cirq.GateFamily(CustomX ** 0.5),
+            cirq.GateFamily(CustomX**0.5),
             cirq.GateFamily(cirq.testing.TwoQubitGate),
             CustomXGateFamily(),
         ]
@@ -214,11 +214,11 @@ def test_gateset_repr_and_str():
     'gate, result',
     [
         (CustomX, True),
-        (CustomX ** 2, True),
+        (CustomX**2, True),
         (CustomXPowGate(exponent=3, global_shift=0.5), True),
-        (CustomX ** 0.5, True),
+        (CustomX**0.5, True),
         (CustomXPowGate(exponent=0.5, global_shift=0.5), True),
-        (CustomX ** 0.25, False),
+        (CustomX**0.25, False),
         (CustomX ** sympy.Symbol('theta'), False),
         (cirq.testing.TwoQubitGate(), True),
     ],
@@ -286,7 +286,7 @@ def test_gateset_validate_circuit_op_negative_reps():
     gate = CustomXPowGate(exponent=0.5)
     op = cirq.CircuitOperation(cirq.FrozenCircuit(gate.on(cirq.LineQubit(0))), repetitions=-1)
     assert op not in cirq.Gateset(gate)
-    assert op ** -1 in cirq.Gateset(gate)
+    assert op**-1 in cirq.Gateset(gate)
 
 
 def test_with_params():
@@ -310,7 +310,7 @@ def test_with_params():
 def test_gateset_eq():
     eq = cirq.testing.EqualsTester()
     eq.add_equality_group(cirq.Gateset(CustomX))
-    eq.add_equality_group(cirq.Gateset(CustomX ** 3))
+    eq.add_equality_group(cirq.Gateset(CustomX**3))
     eq.add_equality_group(cirq.Gateset(CustomX, name='Custom Gateset'))
     eq.add_equality_group(cirq.Gateset(CustomX, name='Custom Gateset', unroll_circuit_op=False))
     eq.add_equality_group(
@@ -322,7 +322,7 @@ def test_gateset_eq():
             cirq.GateFamily(CustomX, name='custom_name', description='custom_description'),
         ),
         cirq.Gateset(
-            cirq.GateFamily(CustomX ** 3, name='custom_name', description='custom_description'),
+            cirq.GateFamily(CustomX**3, name='custom_name', description='custom_description'),
             cirq.GateFamily(CustomX, name='custom_name', description='custom_description'),
         ),
     )
diff --git a/cirq/ops/global_phase_op.py b/cirq/ops/global_phase_op.py
index 139f51ab177..0f5abadf0cc 100644
--- a/cirq/ops/global_phase_op.py
+++ b/cirq/ops/global_phase_op.py
@@ -74,7 +74,7 @@ def _has_unitary_(self) -> bool:
 
     def __pow__(self, power) -> 'cirq.GlobalPhaseGate':
         if isinstance(power, (int, float)):
-            return GlobalPhaseGate(self.coefficient ** power)
+            return GlobalPhaseGate(self.coefficient**power)
         return NotImplemented
 
     def _unitary_(self) -> np.ndarray:
diff --git a/cirq/ops/identity_test.py b/cirq/ops/identity_test.py
index e8f8f409f1b..c1f13a73f88 100644
--- a/cirq/ops/identity_test.py
+++ b/cirq/ops/identity_test.py
@@ -95,9 +95,9 @@ def test_identity_on_each_two_qubits():
 @pytest.mark.parametrize('num_qubits', [1, 2, 4])
 def test_identity_unitary(num_qubits):
     i = cirq.IdentityGate(num_qubits)
-    assert np.allclose(cirq.unitary(i), np.identity(2 ** num_qubits))
+    assert np.allclose(cirq.unitary(i), np.identity(2**num_qubits))
     i3 = cirq.IdentityGate(num_qubits, (3,) * num_qubits)
-    assert np.allclose(cirq.unitary(i3), np.identity(3 ** num_qubits))
+    assert np.allclose(cirq.unitary(i3), np.identity(3**num_qubits))
 
 
 def test_identity_str():
@@ -153,7 +153,7 @@ def test_identity_pow():
     assert I(q) ** (1 + 1j) == I(q)
     assert I(q) ** sympy.Symbol('x') == I(q)
     with pytest.raises(TypeError):
-        _ = (I ** q)(q)
+        _ = (I**q)(q)
     with pytest.raises(TypeError):
         _ = I(q) ** q
 
diff --git a/cirq/ops/linear_combinations.py b/cirq/ops/linear_combinations.py
index 90a27f724be..3249d8ef512 100644
--- a/cirq/ops/linear_combinations.py
+++ b/cirq/ops/linear_combinations.py
@@ -179,7 +179,7 @@ def matrix(self) -> np.ndarray:
         num_qubits = self.num_qubits()
         if num_qubits is None:
             raise ValueError('Unknown number of qubits')
-        num_dim = 2 ** num_qubits
+        num_dim = 2**num_qubits
         result = np.zeros((num_dim, num_dim), dtype=np.complex128)
         for gate, coefficient in self.items():
             result += protocols.unitary(gate) * coefficient
@@ -292,7 +292,7 @@ def matrix(self) -> np.ndarray:
         if self._is_parameterized_():
             return NotImplemented
         num_qubits = len(self.qubits)
-        num_dim = 2 ** num_qubits
+        num_dim = 2**num_qubits
         qubit_to_axis = {q: i for i, q in enumerate(self.qubits)}
         result = np.zeros((2,) * (2 * num_qubits), dtype=np.complex128)
         for op, coefficient in self.items():
@@ -487,7 +487,7 @@ def matrix(self, qubits: Optional[Iterable[raw_types.Qid]] = None) -> np.ndarray
 
         qubits = self.qubits if qubits is None else tuple(qubits)
         num_qubits = len(qubits)
-        num_dim = 2 ** num_qubits
+        num_dim = 2**num_qubits
         result = np.zeros((num_dim, num_dim), dtype=np.complex128)
         for vec, coeff in self._linear_dict.items():
             op = _pauli_string_from_unit(vec)
diff --git a/cirq/ops/linear_combinations_test.py b/cirq/ops/linear_combinations_test.py
index 4282abb9021..74e88bed551 100644
--- a/cirq/ops/linear_combinations_test.py
+++ b/cirq/ops/linear_combinations_test.py
@@ -203,7 +203,7 @@ def test_linear_combination_of_gates_has_correct_pauli_expansion(terms, expected
             },
             10,
             {
-                cirq.I: 2 ** -10,
+                cirq.I: 2**-10,
             },
         ),
         (
@@ -212,7 +212,7 @@ def test_linear_combination_of_gates_has_correct_pauli_expansion(terms, expected
             },
             11,
             {
-                cirq.Y: 2 ** -11,
+                cirq.Y: 2**-11,
             },
         ),
         (
@@ -252,7 +252,7 @@ def test_linear_combination_of_gates_has_correct_pauli_expansion(terms, expected
 )
 def test_linear_combinations_of_gates_valid_powers(terms, exponent, expected_terms):
     combination = cirq.LinearCombinationOfGates(terms)
-    actual_result = combination ** exponent
+    actual_result = combination**exponent
     expected_result = cirq.LinearCombinationOfGates(expected_terms)
     assert cirq.approx_eq(actual_result, expected_result)
     assert len(actual_result) == len(expected_terms)
@@ -298,7 +298,7 @@ def test_linear_combinations_of_gates_valid_powers(terms, exponent, expected_ter
 def test_linear_combinations_of_gates_invalid_powers(terms, exponent):
     combination = cirq.LinearCombinationOfGates(terms)
     with pytest.raises(TypeError):
-        _ = combination ** exponent
+        _ = combination**exponent
 
 
 @pytest.mark.parametrize(
@@ -792,7 +792,7 @@ def test_linear_combination_of_operations_has_correct_pauli_expansion(terms, exp
             },
             10,
             {
-                cirq.I(q0): 2 ** -10,
+                cirq.I(q0): 2**-10,
             },
         ),
         (
@@ -801,7 +801,7 @@ def test_linear_combination_of_operations_has_correct_pauli_expansion(terms, exp
             },
             11,
             {
-                cirq.Y(q0): 2 ** -11,
+                cirq.Y(q0): 2**-11,
             },
         ),
         (
@@ -841,7 +841,7 @@ def test_linear_combination_of_operations_has_correct_pauli_expansion(terms, exp
 )
 def test_linear_combinations_of_operations_valid_powers(terms, exponent, expected_terms):
     combination = cirq.LinearCombinationOfOperations(terms)
-    actual_result = combination ** exponent
+    actual_result = combination**exponent
     expected_result = cirq.LinearCombinationOfOperations(expected_terms)
     assert cirq.approx_eq(actual_result, expected_result)
     assert len(actual_result) == len(expected_terms)
@@ -894,7 +894,7 @@ def test_linear_combinations_of_operations_valid_powers(terms, exponent, expecte
 def test_linear_combinations_of_operations_invalid_powers(terms, exponent):
     combination = cirq.LinearCombinationOfOperations(terms)
     with pytest.raises(TypeError):
-        _ = combination ** exponent
+        _ = combination**exponent
 
 
 @pytest.mark.parametrize(
@@ -1262,10 +1262,10 @@ def test_bad_arithmetic():
         _ = psum / [1, 2, 3]
 
     with pytest.raises(TypeError):
-        _ = psum ** 1.2
+        _ = psum**1.2
 
     with pytest.raises(TypeError):
-        _ = psum ** -2
+        _ = psum**-2
 
     with pytest.raises(TypeError):
         _ = psum ** "string"
@@ -1333,24 +1333,24 @@ def test_paulisum_mul_paulisum():
 def test_pauli_sum_pow():
     identity = cirq.PauliSum.from_pauli_strings([cirq.PauliString(coefficient=1)])
     psum1 = cirq.X(q0) + cirq.Y(q0)
-    assert psum1 ** 2 == psum1 * psum1
-    assert psum1 ** 2 == 2 * identity
+    assert psum1**2 == psum1 * psum1
+    assert psum1**2 == 2 * identity
 
     psum2 = cirq.X(q0) + cirq.Y(q1)
-    assert psum2 ** 2 == cirq.PauliString(cirq.I(q0)) + 2 * cirq.X(q0) * cirq.Y(
+    assert psum2**2 == cirq.PauliString(cirq.I(q0)) + 2 * cirq.X(q0) * cirq.Y(
         q1
     ) + cirq.PauliString(cirq.I(q1))
 
     psum3 = cirq.X(q0) * cirq.Z(q1) + 1.3 * cirq.Z(q0)
     sqd = cirq.PauliSum.from_pauli_strings([2.69 * cirq.PauliString(cirq.I(q0))])
-    assert cirq.approx_eq(psum3 ** 2, sqd, atol=1e-8)
+    assert cirq.approx_eq(psum3**2, sqd, atol=1e-8)
 
     psum4 = cirq.X(q0) * cirq.Z(q1) + 1.3 * cirq.Z(q1)
     sqd2 = cirq.PauliSum.from_pauli_strings([2.69 * cirq.PauliString(cirq.I(q0)), 2.6 * cirq.X(q0)])
-    assert cirq.approx_eq(psum4 ** 2, sqd2, atol=1e-8)
+    assert cirq.approx_eq(psum4**2, sqd2, atol=1e-8)
 
     for psum in [psum1, psum2, psum3, psum4]:
-        assert cirq.approx_eq(psum ** 0, identity)
+        assert cirq.approx_eq(psum**0, identity)
 
 
 # Using the entries of table 1 of https://arxiv.org/abs/1804.09130 as golden values.
diff --git a/cirq/ops/matrix_gates.py b/cirq/ops/matrix_gates.py
index 998df1948ba..bb6d53207fe 100644
--- a/cirq/ops/matrix_gates.py
+++ b/cirq/ops/matrix_gates.py
@@ -71,7 +71,7 @@ def __init__(
 
         if qid_shape is None:
             n = int(np.round(np.log2(matrix.shape[0] or 1)))
-            if 2 ** n != matrix.shape[0]:
+            if 2**n != matrix.shape[0]:
                 raise ValueError(
                     f'Matrix width ({matrix.shape[0]}) is not a power of 2 and '
                     f'qid_shape is not specified.'
@@ -109,7 +109,7 @@ def __pow__(self, exponent: Any) -> 'MatrixGate':
         if not isinstance(exponent, (int, float)):
             return NotImplemented
         e = cast(float, exponent)
-        new_mat = linalg.map_eigenvalues(self._matrix, lambda b: b ** e)
+        new_mat = linalg.map_eigenvalues(self._matrix, lambda b: b**e)
         return MatrixGate(new_mat, qid_shape=self._qid_shape)
 
     def _phase_by_(self, phase_turns: float, qubit_index: int) -> 'MatrixGate':
diff --git a/cirq/ops/matrix_gates_test.py b/cirq/ops/matrix_gates_test.py
index 848e685022d..0e66df1f4d0 100644
--- a/cirq/ops/matrix_gates_test.py
+++ b/cirq/ops/matrix_gates_test.py
@@ -80,16 +80,16 @@ def test_single_qubit_extrapolate():
     assert cirq.has_unitary(x2)
     x2i = cirq.MatrixGate(np.conj(cirq.unitary(x2).T))
 
-    assert cirq.approx_eq(x ** 0, i, atol=1e-9)
-    assert cirq.approx_eq(x2 ** 0, i, atol=1e-9)
-    assert cirq.approx_eq(x2 ** 2, x, atol=1e-9)
-    assert cirq.approx_eq(x2 ** -1, x2i, atol=1e-9)
-    assert cirq.approx_eq(x2 ** 3, x2i, atol=1e-9)
-    assert cirq.approx_eq(x ** -1, x, atol=1e-9)
+    assert cirq.approx_eq(x**0, i, atol=1e-9)
+    assert cirq.approx_eq(x2**0, i, atol=1e-9)
+    assert cirq.approx_eq(x2**2, x, atol=1e-9)
+    assert cirq.approx_eq(x2**-1, x2i, atol=1e-9)
+    assert cirq.approx_eq(x2**3, x2i, atol=1e-9)
+    assert cirq.approx_eq(x**-1, x, atol=1e-9)
 
     z2 = cirq.MatrixGate(np.array([[1, 0], [0, 1j]]))
     z4 = cirq.MatrixGate(np.array([[1, 0], [0, (1 + 1j) * np.sqrt(0.5)]]))
-    assert cirq.approx_eq(z2 ** 0.5, z4, atol=1e-9)
+    assert cirq.approx_eq(z2**0.5, z4, atol=1e-9)
     with pytest.raises(TypeError):
         _ = x ** sympy.Symbol('a')
 
@@ -125,9 +125,9 @@ def test_two_qubit_extrapolate():
     cz4 = cirq.MatrixGate(np.diag([1, 1, 1, (1 + 1j) * np.sqrt(0.5)]))
     i = cirq.MatrixGate(np.eye(4))
 
-    assert cirq.approx_eq(cz2 ** 0, i, atol=1e-9)
-    assert cirq.approx_eq(cz4 ** 0, i, atol=1e-9)
-    assert cirq.approx_eq(cz2 ** 0.5, cz4, atol=1e-9)
+    assert cirq.approx_eq(cz2**0, i, atol=1e-9)
+    assert cirq.approx_eq(cz4**0, i, atol=1e-9)
+    assert cirq.approx_eq(cz2**0.5, cz4, atol=1e-9)
     with pytest.raises(TypeError):
         _ = cz2 ** sympy.Symbol('a')
 
@@ -278,7 +278,7 @@ def test_str_executes():
 
 @pytest.mark.parametrize('n', [1, 2, 3, 4, 5])
 def test_implements_consistent_protocols(n):
-    u = cirq.testing.random_unitary(2 ** n)
+    u = cirq.testing.random_unitary(2**n)
     g1 = cirq.MatrixGate(u)
     cirq.testing.assert_implements_consistent_protocols(g1, ignoring_global_phase=True)
     cirq.testing.assert_decompose_ends_at_default_gateset(g1)
@@ -323,7 +323,7 @@ def test_matrix_gate_pow():
     assert cirq.pow(cirq.MatrixGate(1j * np.eye(1)), 2) == cirq.MatrixGate(-np.eye(1))
 
     m = cirq.MatrixGate(np.diag([1, 1j, -1]), qid_shape=(3,))
-    assert m ** 3 == cirq.MatrixGate(np.diag([1, -1j, -1]), qid_shape=(3,))
+    assert m**3 == cirq.MatrixGate(np.diag([1, -1j, -1]), qid_shape=(3,))
 
 
 def test_phase_by():
diff --git a/cirq/ops/measurement_gate_test.py b/cirq/ops/measurement_gate_test.py
index e281fb71123..94ac510dae6 100644
--- a/cirq/ops/measurement_gate_test.py
+++ b/cirq/ops/measurement_gate_test.py
@@ -173,19 +173,16 @@ def test_measurement_gate_diagram():
     ) == cirq.CircuitDiagramInfo(("M('test')",))
 
     # Uses known qubit count.
-    assert (
-        cirq.circuit_diagram_info(
-            cirq.MeasurementGate(3, 'a'),
-            cirq.CircuitDiagramInfoArgs(
-                known_qubits=None,
-                known_qubit_count=3,
-                use_unicode_characters=True,
-                precision=None,
-                label_map=None,
-            ),
-        )
-        == cirq.CircuitDiagramInfo(("M('a')", 'M', 'M'))
-    )
+    assert cirq.circuit_diagram_info(
+        cirq.MeasurementGate(3, 'a'),
+        cirq.CircuitDiagramInfoArgs(
+            known_qubits=None,
+            known_qubit_count=3,
+            use_unicode_characters=True,
+            precision=None,
+            label_map=None,
+        ),
+    ) == cirq.CircuitDiagramInfo(("M('a')", 'M', 'M'))
 
     # Shows invert mask.
     assert cirq.circuit_diagram_info(
diff --git a/cirq/ops/parallel_gate_test.py b/cirq/ops/parallel_gate_test.py
index 814f5a3951e..b2d807b90cd 100644
--- a/cirq/ops/parallel_gate_test.py
+++ b/cirq/ops/parallel_gate_test.py
@@ -22,7 +22,7 @@
     'gate, num_copies, qubits',
     [
         (cirq.SingleQubitGate(), 2, cirq.LineQubit.range(2)),
-        (cirq.X ** 0.5, 4, cirq.LineQubit.range(4)),
+        (cirq.X**0.5, 4, cirq.LineQubit.range(4)),
     ],
 )
 def test_parallel_gate_operation_init(gate, num_copies, qubits):
@@ -50,7 +50,7 @@ def test_invalid_parallel_gate_operation(gate, num_copies, qubits, error_msg):
     'gate, num_copies, qubits',
     [
         (cirq.X, 2, cirq.LineQubit.range(2)),
-        (cirq.H ** 0.5, 4, cirq.LineQubit.range(4)),
+        (cirq.H**0.5, 4, cirq.LineQubit.range(4)),
     ],
 )
 def test_decompose(gate, num_copies, qubits):
@@ -77,11 +77,11 @@ def test_extrapolate():
     # If the gate isn't extrapolatable, you get a type error.
     g = cirq.ParallelGate(cirq.SingleQubitGate(), 2)
     with pytest.raises(TypeError):
-        _ = g ** 0.5
+        _ = g**0.5
     # If the gate is extrapolatable, the effect is applied on the underlying gate.
     g = cirq.ParallelGate(cirq.Y, 2)
-    assert g ** 0.5 == cirq.ParallelGate(cirq.Y ** 0.5, 2)
-    assert cirq.inverse(g) == g ** -1 == cirq.ParallelGate(cirq.Y ** -1, 2)
+    assert g**0.5 == cirq.ParallelGate(cirq.Y**0.5, 2)
+    assert cirq.inverse(g) == g**-1 == cirq.ParallelGate(cirq.Y**-1, 2)
 
 
 @pytest.mark.parametrize('resolve_fn', [cirq.resolve_parameters, cirq.resolve_parameters_once])
@@ -103,8 +103,8 @@ def test_no_unitary(gate):
 @pytest.mark.parametrize(
     'gate, num_copies, qubits',
     [
-        (cirq.X ** 0.5, 2, cirq.LineQubit.range(2)),
-        (cirq.MatrixGate(cirq.unitary(cirq.H ** 0.25)), 6, cirq.LineQubit.range(6)),
+        (cirq.X**0.5, 2, cirq.LineQubit.range(2)),
+        (cirq.MatrixGate(cirq.unitary(cirq.H**0.25)), 6, cirq.LineQubit.range(6)),
     ],
 )
 def test_unitary(gate, num_copies, qubits):
@@ -131,14 +131,14 @@ def test_repr():
 
 
 def test_str():
-    assert str(cirq.ParallelGate(cirq.X ** 0.5, 10)) == 'X**0.5 x 10'
+    assert str(cirq.ParallelGate(cirq.X**0.5, 10)) == 'X**0.5 x 10'
 
 
 def test_equivalent_circuit():
     qreg = cirq.LineQubit.range(4)
     oldc = cirq.Circuit()
     newc = cirq.Circuit()
-    single_qubit_gates = [cirq.X ** (1 / 2), cirq.Y ** (1 / 3), cirq.Z ** -1]
+    single_qubit_gates = [cirq.X ** (1 / 2), cirq.Y ** (1 / 3), cirq.Z**-1]
     for gate in single_qubit_gates:
         for qubit in qreg:
             oldc.append(gate.on(qubit))
@@ -161,7 +161,7 @@ def test_parallel_gate_operation_is_consistent(gate, num_copies):
 
 
 def test_trace_distance():
-    s = cirq.X ** 0.25
+    s = cirq.X**0.25
     two_g = cirq.ParallelGate(s, 2)
     three_g = cirq.ParallelGate(s, 3)
     four_g = cirq.ParallelGate(s, 4)
diff --git a/cirq/ops/parity_gates_test.py b/cirq/ops/parity_gates_test.py
index 19c11676efc..f04502fa3b9 100644
--- a/cirq/ops/parity_gates_test.py
+++ b/cirq/ops/parity_gates_test.py
@@ -47,23 +47,23 @@ def test_xx_eq():
         cirq.XXPowGate(exponent=1, global_shift=0),
         cirq.XXPowGate(exponent=3, global_shift=0),
     )
-    eq.add_equality_group(cirq.XX ** 0.5, cirq.XX ** 2.5, cirq.XX ** 4.5)
-    eq.add_equality_group(cirq.XX ** 0.25, cirq.XX ** 2.25, cirq.XX ** -1.75)
+    eq.add_equality_group(cirq.XX**0.5, cirq.XX**2.5, cirq.XX**4.5)
+    eq.add_equality_group(cirq.XX**0.25, cirq.XX**2.25, cirq.XX**-1.75)
 
     iXX = cirq.XXPowGate(global_shift=0.5)
-    eq.add_equality_group(iXX ** 0.5, iXX ** 4.5)
-    eq.add_equality_group(iXX ** 2.5, iXX ** 6.5)
+    eq.add_equality_group(iXX**0.5, iXX**4.5)
+    eq.add_equality_group(iXX**2.5, iXX**6.5)
 
 
 def test_xx_pow():
-    assert cirq.XX ** 0.5 != cirq.XX ** -0.5
-    assert cirq.XX ** -1 == cirq.XX
-    assert (cirq.XX ** -1) ** 0.5 == cirq.XX ** -0.5
+    assert cirq.XX**0.5 != cirq.XX**-0.5
+    assert cirq.XX**-1 == cirq.XX
+    assert (cirq.XX**-1) ** 0.5 == cirq.XX**-0.5
 
 
 def test_xx_str():
     assert str(cirq.XX) == 'XX'
-    assert str(cirq.XX ** 0.5) == 'XX**0.5'
+    assert str(cirq.XX**0.5) == 'XX**0.5'
     assert str(cirq.XXPowGate(global_shift=0.1)) == 'XX'
 
 
@@ -78,7 +78,7 @@ def test_xx_matrix():
         np.array([[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]]),
         atol=1e-8,
     )
-    np.testing.assert_allclose(cirq.unitary(cirq.XX ** 2), np.eye(4), atol=1e-8)
+    np.testing.assert_allclose(cirq.unitary(cirq.XX**2), np.eye(4), atol=1e-8)
     c = np.cos(np.pi / 6)
     s = -1j * np.sin(np.pi / 6)
     np.testing.assert_allclose(
@@ -120,23 +120,23 @@ def test_yy_eq():
         cirq.YYPowGate(exponent=1, global_shift=0),
         cirq.YYPowGate(exponent=3, global_shift=0),
     )
-    eq.add_equality_group(cirq.YY ** 0.5, cirq.YY ** 2.5, cirq.YY ** 4.5)
-    eq.add_equality_group(cirq.YY ** 0.25, cirq.YY ** 2.25, cirq.YY ** -1.75)
+    eq.add_equality_group(cirq.YY**0.5, cirq.YY**2.5, cirq.YY**4.5)
+    eq.add_equality_group(cirq.YY**0.25, cirq.YY**2.25, cirq.YY**-1.75)
 
     iYY = cirq.YYPowGate(global_shift=0.5)
-    eq.add_equality_group(iYY ** 0.5, iYY ** 4.5)
-    eq.add_equality_group(iYY ** 2.5, iYY ** 6.5)
+    eq.add_equality_group(iYY**0.5, iYY**4.5)
+    eq.add_equality_group(iYY**2.5, iYY**6.5)
 
 
 def test_yy_pow():
-    assert cirq.YY ** 0.5 != cirq.YY ** -0.5
-    assert cirq.YY ** -1 == cirq.YY
-    assert (cirq.YY ** -1) ** 0.5 == cirq.YY ** -0.5
+    assert cirq.YY**0.5 != cirq.YY**-0.5
+    assert cirq.YY**-1 == cirq.YY
+    assert (cirq.YY**-1) ** 0.5 == cirq.YY**-0.5
 
 
 def test_yy_str():
     assert str(cirq.YY) == 'YY'
-    assert str(cirq.YY ** 0.5) == 'YY**0.5'
+    assert str(cirq.YY**0.5) == 'YY**0.5'
     assert str(cirq.YYPowGate(global_shift=0.1)) == 'YY'
 
     iYY = cirq.YYPowGate(global_shift=0.5)
@@ -154,7 +154,7 @@ def test_yy_matrix():
         np.array([[0, 0, 0, -1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, 0, 0, 0]]),
         atol=1e-8,
     )
-    np.testing.assert_allclose(cirq.unitary(cirq.YY ** 2), np.eye(4), atol=1e-8)
+    np.testing.assert_allclose(cirq.unitary(cirq.YY**2), np.eye(4), atol=1e-8)
     c = np.cos(np.pi / 6)
     s = 1j * np.sin(np.pi / 6)
     np.testing.assert_allclose(
@@ -196,23 +196,23 @@ def test_zz_eq():
         cirq.ZZPowGate(exponent=1, global_shift=0),
         cirq.ZZPowGate(exponent=3, global_shift=0),
     )
-    eq.add_equality_group(cirq.ZZ ** 0.5, cirq.ZZ ** 2.5, cirq.ZZ ** 4.5)
-    eq.add_equality_group(cirq.ZZ ** 0.25, cirq.ZZ ** 2.25, cirq.ZZ ** -1.75)
+    eq.add_equality_group(cirq.ZZ**0.5, cirq.ZZ**2.5, cirq.ZZ**4.5)
+    eq.add_equality_group(cirq.ZZ**0.25, cirq.ZZ**2.25, cirq.ZZ**-1.75)
 
     iZZ = cirq.ZZPowGate(global_shift=0.5)
-    eq.add_equality_group(iZZ ** 0.5, iZZ ** 4.5)
-    eq.add_equality_group(iZZ ** 2.5, iZZ ** 6.5)
+    eq.add_equality_group(iZZ**0.5, iZZ**4.5)
+    eq.add_equality_group(iZZ**2.5, iZZ**6.5)
 
 
 def test_zz_pow():
-    assert cirq.ZZ ** 0.5 != cirq.ZZ ** -0.5
-    assert cirq.ZZ ** -1 == cirq.ZZ
-    assert (cirq.ZZ ** -1) ** 0.5 == cirq.ZZ ** -0.5
+    assert cirq.ZZ**0.5 != cirq.ZZ**-0.5
+    assert cirq.ZZ**-1 == cirq.ZZ
+    assert (cirq.ZZ**-1) ** 0.5 == cirq.ZZ**-0.5
 
 
 def test_zz_str():
     assert str(cirq.ZZ) == 'ZZ'
-    assert str(cirq.ZZ ** 0.5) == 'ZZ**0.5'
+    assert str(cirq.ZZ**0.5) == 'ZZ**0.5'
     assert str(cirq.ZZPowGate(global_shift=0.1)) == 'ZZ'
 
     iZZ = cirq.ZZPowGate(global_shift=0.5)
@@ -230,8 +230,8 @@ def test_zz_matrix():
         np.array([[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]]),
         atol=1e-8,
     )
-    np.testing.assert_allclose(cirq.unitary(cirq.ZZ ** 2), np.eye(4), atol=1e-8)
-    b = 1j ** 0.25
+    np.testing.assert_allclose(cirq.unitary(cirq.ZZ**2), np.eye(4), atol=1e-8)
+    b = 1j**0.25
     a = np.conj(b)
     np.testing.assert_allclose(
         cirq.unitary(cirq.ZZPowGate(exponent=0.25, global_shift=-0.5)),
@@ -260,9 +260,9 @@ def test_zz_diagrams():
 
 def test_trace_distance():
     foo = sympy.Symbol('foo')
-    assert cirq.trace_distance_bound(cirq.XX ** foo) == 1.0
-    assert cirq.trace_distance_bound(cirq.YY ** foo) == 1.0
-    assert cirq.trace_distance_bound(cirq.ZZ ** foo) == 1.0
+    assert cirq.trace_distance_bound(cirq.XX**foo) == 1.0
+    assert cirq.trace_distance_bound(cirq.YY**foo) == 1.0
+    assert cirq.trace_distance_bound(cirq.ZZ**foo) == 1.0
     assert cirq.approx_eq(cirq.trace_distance_bound(cirq.XX), 1.0)
-    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.YY ** 0), 0)
+    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.YY**0), 0)
     assert cirq.approx_eq(cirq.trace_distance_bound(cirq.ZZ ** (1 / 3)), np.sin(np.pi / 6))
diff --git a/cirq/ops/pauli_gates_test.py b/cirq/ops/pauli_gates_test.py
index 81753b5f019..c6a03e3f3f5 100644
--- a/cirq/ops/pauli_gates_test.py
+++ b/cirq/ops/pauli_gates_test.py
@@ -210,13 +210,13 @@ def test_powers():
     assert isinstance(cirq.X, cirq.Pauli)
     assert isinstance(cirq.Y, cirq.Pauli)
     assert isinstance(cirq.Z, cirq.Pauli)
-    assert not isinstance(cirq.X ** -0.5, cirq.Pauli)
-    assert not isinstance(cirq.Y ** 0.2, cirq.Pauli)
-    assert not isinstance(cirq.Z ** 0.5, cirq.Pauli)
-    assert isinstance(cirq.X ** -0.5, cirq.XPowGate)
-    assert isinstance(cirq.Y ** 0.2, cirq.YPowGate)
-    assert isinstance(cirq.Z ** 0.5, cirq.ZPowGate)
-
-    assert isinstance(cirq.X ** 1, cirq.Pauli)
-    assert isinstance(cirq.Y ** 1, cirq.Pauli)
-    assert isinstance(cirq.Z ** 1, cirq.Pauli)
+    assert not isinstance(cirq.X**-0.5, cirq.Pauli)
+    assert not isinstance(cirq.Y**0.2, cirq.Pauli)
+    assert not isinstance(cirq.Z**0.5, cirq.Pauli)
+    assert isinstance(cirq.X**-0.5, cirq.XPowGate)
+    assert isinstance(cirq.Y**0.2, cirq.YPowGate)
+    assert isinstance(cirq.Z**0.5, cirq.ZPowGate)
+
+    assert isinstance(cirq.X**1, cirq.Pauli)
+    assert isinstance(cirq.Y**1, cirq.Pauli)
+    assert isinstance(cirq.Z**1, cirq.Pauli)
diff --git a/cirq/ops/pauli_interaction_gate.py b/cirq/ops/pauli_interaction_gate.py
index 5a0a27df8fa..23c464d6a6c 100644
--- a/cirq/ops/pauli_interaction_gate.py
+++ b/cirq/ops/pauli_interaction_gate.py
@@ -151,8 +151,8 @@ def _decompose_(self, qubits: Sequence['cirq.Qid']) -> 'cirq.OP_TREE':
         right_gate0 = SingleQubitCliffordGate.from_single_map(z_to=(self.pauli0, self.invert0))
         right_gate1 = SingleQubitCliffordGate.from_single_map(z_to=(self.pauli1, self.invert1))
 
-        left_gate0 = right_gate0 ** -1
-        left_gate1 = right_gate1 ** -1
+        left_gate0 = right_gate0**-1
+        left_gate1 = right_gate1**-1
         yield left_gate0(q0)
         yield left_gate1(q1)
         yield common_gates.CZ(q0, q1) ** self._exponent
diff --git a/cirq/ops/pauli_interaction_gate_test.py b/cirq/ops/pauli_interaction_gate_test.py
index 4a7eb6fde98..7af7206457d 100644
--- a/cirq/ops/pauli_interaction_gate_test.py
+++ b/cirq/ops/pauli_interaction_gate_test.py
@@ -82,7 +82,7 @@ def test_interchangeable_qubits(gate):
 def test_exponent():
     cnot = cirq.PauliInteractionGate(cirq.Z, False, cirq.X, False)
     np.testing.assert_almost_equal(
-        cirq.unitary(cnot ** 0.5),
+        cirq.unitary(cnot**0.5),
         np.array(
             [
                 [1, 0, 0, 0],
diff --git a/cirq/ops/pauli_measurement_gate_test.py b/cirq/ops/pauli_measurement_gate_test.py
index 533e87f9b21..451058f9e6f 100644
--- a/cirq/ops/pauli_measurement_gate_test.py
+++ b/cirq/ops/pauli_measurement_gate_test.py
@@ -185,10 +185,10 @@ def test_with_observable():
     [
         (cirq.I, cirq.DensePauliString("Z", coefficient=+1), 0),
         (cirq.I, cirq.DensePauliString("Z", coefficient=-1), 1),
-        (cirq.Y ** 0.5, cirq.DensePauliString("X", coefficient=+1), 0),
-        (cirq.Y ** 0.5, cirq.DensePauliString("X", coefficient=-1), 1),
-        (cirq.X ** -0.5, cirq.DensePauliString("Y", coefficient=+1), 0),
-        (cirq.X ** -0.5, cirq.DensePauliString("Y", coefficient=-1), 1),
+        (cirq.Y**0.5, cirq.DensePauliString("X", coefficient=+1), 0),
+        (cirq.Y**0.5, cirq.DensePauliString("X", coefficient=-1), 1),
+        (cirq.X**-0.5, cirq.DensePauliString("Y", coefficient=+1), 0),
+        (cirq.X**-0.5, cirq.DensePauliString("Y", coefficient=-1), 1),
     ],
 )
 def test_pauli_measurement_gate_samples(rot, obs, out):
diff --git a/cirq/ops/pauli_string.py b/cirq/ops/pauli_string.py
index 9a44cc78176..9d146639143 100644
--- a/cirq/ops/pauli_string.py
+++ b/cirq/ops/pauli_string.py
@@ -693,7 +693,7 @@ def __pos__(self) -> 'PauliString':
     def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
         """Override behavior of numpy's exp method."""
         if ufunc == np.exp and len(inputs) == 1 and inputs[0] is self:
-            return math.e ** self
+            return math.e**self
         return NotImplemented
 
     def __pow__(self, power):
@@ -701,7 +701,7 @@ def __pow__(self, power):
             return self
         if power == -1:
             return PauliString(
-                qubit_pauli_map=self._qubit_pauli_map, coefficient=self.coefficient ** -1
+                qubit_pauli_map=self._qubit_pauli_map, coefficient=self.coefficient**-1
             )
         if isinstance(power, (int, float)):
             r, i = cmath.polar(self.coefficient)
diff --git a/cirq/ops/pauli_string_phasor.py b/cirq/ops/pauli_string_phasor.py
index aa761f5d503..75a7aa19861 100644
--- a/cirq/ops/pauli_string_phasor.py
+++ b/cirq/ops/pauli_string_phasor.py
@@ -334,7 +334,7 @@ def _decompose_(self, qubits: Sequence['cirq.Qid']) -> 'cirq.OP_TREE':
     def _trace_distance_bound_(self) -> float:
         if len(self.dense_pauli_string) == 0:
             return 0.0
-        return protocols.trace_distance_bound(pauli_gates.Z ** self.exponent_relative)
+        return protocols.trace_distance_bound(pauli_gates.Z**self.exponent_relative)
 
     def _is_parameterized_(self) -> bool:
         return protocols.is_parameterized(self.exponent_neg) or protocols.is_parameterized(
diff --git a/cirq/ops/pauli_string_phasor_test.py b/cirq/ops/pauli_string_phasor_test.py
index d2f72921520..6e0e97fe79d 100644
--- a/cirq/ops/pauli_string_phasor_test.py
+++ b/cirq/ops/pauli_string_phasor_test.py
@@ -110,10 +110,10 @@ def test_pow():
     a = cirq.LineQubit(0)
     s = cirq.PauliString({a: cirq.X})
     p = cirq.PauliStringPhasor(s, exponent_neg=0.25, exponent_pos=0.5)
-    assert p ** 0.5 == cirq.PauliStringPhasor(s, exponent_neg=0.125, exponent_pos=0.25)
+    assert p**0.5 == cirq.PauliStringPhasor(s, exponent_neg=0.125, exponent_pos=0.25)
     with pytest.raises(TypeError, match='unsupported operand'):
         _ = p ** object()
-    assert p ** 1 == p
+    assert p**1 == p
 
 
 def test_consistent():
@@ -139,8 +139,8 @@ def test_extrapolate_effect():
     op1 = cirq.PauliStringPhasor(cirq.PauliString({}), exponent_neg=0.5)
     op2 = cirq.PauliStringPhasor(cirq.PauliString({}), exponent_neg=1.5)
     op3 = cirq.PauliStringPhasor(cirq.PauliString({}), exponent_neg=0.125)
-    assert op1 ** 3 == op2
-    assert op1 ** 0.25 == op3
+    assert op1**3 == op2
+    assert op1**0.25 == op3
 
 
 def test_extrapolate_effect_with_symbol():
@@ -225,7 +225,7 @@ def test_merge_with():
 def test_is_parameterized():
     op = cirq.PauliStringPhasor(cirq.PauliString({}))
     assert not cirq.is_parameterized(op)
-    assert not cirq.is_parameterized(op ** 0.1)
+    assert not cirq.is_parameterized(op**0.1)
     assert cirq.is_parameterized(op ** sympy.Symbol('a'))
 
 
@@ -322,8 +322,8 @@ def test_default_decompose(paulis, phase_exponent_negative: float, sign: int):
 
     # Calculate expected matrix
     to_z_mats = {
-        cirq.X: cirq.unitary(cirq.Y ** -0.5),
-        cirq.Y: cirq.unitary(cirq.X ** 0.5),
+        cirq.X: cirq.unitary(cirq.Y**-0.5),
+        cirq.Y: cirq.unitary(cirq.X**0.5),
         cirq.Z: np.eye(2),
     }
     expected_convert = np.eye(1)
@@ -503,18 +503,18 @@ def test_gate_equal_up_to_global_phase():
 def test_gate_pow():
     s = dps_x
     p = cirq.PauliStringPhasorGate(s, exponent_neg=0.25, exponent_pos=0.5)
-    assert p ** 0.5 == cirq.PauliStringPhasorGate(s, exponent_neg=0.125, exponent_pos=0.25)
+    assert p**0.5 == cirq.PauliStringPhasorGate(s, exponent_neg=0.125, exponent_pos=0.25)
     with pytest.raises(TypeError, match='unsupported operand'):
         _ = p ** object()
-    assert p ** 1 == p
+    assert p**1 == p
 
 
 def test_gate_extrapolate_effect():
     gate1 = cirq.PauliStringPhasorGate(dps_empty, exponent_neg=0.5)
     gate2 = cirq.PauliStringPhasorGate(dps_empty, exponent_neg=1.5)
     gate3 = cirq.PauliStringPhasorGate(dps_empty, exponent_neg=0.125)
-    assert gate1 ** 3 == gate2
-    assert gate1 ** 0.25 == gate3
+    assert gate1**3 == gate2
+    assert gate1**0.25 == gate3
 
 
 def test_gate_extrapolate_effect_with_symbol():
@@ -548,7 +548,7 @@ def test_gate_inverse():
 def test_gate_is_parameterized():
     gate = cirq.PauliStringPhasorGate(dps_empty)
     assert not cirq.is_parameterized(gate)
-    assert not cirq.is_parameterized(gate ** 0.1)
+    assert not cirq.is_parameterized(gate**0.1)
     assert cirq.is_parameterized(gate ** sympy.Symbol('a'))
 
 
diff --git a/cirq/ops/pauli_string_test.py b/cirq/ops/pauli_string_test.py
index 04f4fd8785f..5c748903045 100644
--- a/cirq/ops/pauli_string_test.py
+++ b/cirq/ops/pauli_string_test.py
@@ -172,13 +172,13 @@ def test_exponentiation_as_base():
         _ = p ** 'test'
 
     with pytest.raises(TypeError, match='unsupported'):
-        _ = p ** 1j
+        _ = p**1j
 
-    assert p ** -1 == p
+    assert p**-1 == p
 
-    assert cirq.approx_eq(p ** 0.5, cirq.PauliStringPhasor(p, exponent_neg=0.5, exponent_pos=0))
+    assert cirq.approx_eq(p**0.5, cirq.PauliStringPhasor(p, exponent_neg=0.5, exponent_pos=0))
 
-    assert cirq.approx_eq(p ** -0.5, cirq.PauliStringPhasor(p, exponent_neg=-0.5, exponent_pos=0))
+    assert cirq.approx_eq(p**-0.5, cirq.PauliStringPhasor(p, exponent_neg=-0.5, exponent_pos=0))
 
     assert cirq.approx_eq(
         math.e ** (0.25j * math.pi * p),
@@ -535,8 +535,8 @@ def test_pow():
     assert cirq.PauliString({a: cirq.Z}) ** 0.25 == cirq.Z(a) ** 0.25
 
     p = cirq.PauliString({a: cirq.X, b: cirq.Y})
-    assert p ** 1 == p
-    assert p ** -1 == p
+    assert p**1 == p
+    assert p**-1 == p
     assert (-p) ** 1 == -p
     assert (-p) ** -1 == -p
     assert (1j * p) ** 1 == 1j * p
@@ -593,7 +593,7 @@ def test_to_z_basis_ops():
     initial_state = cirq.kron(x0, x1, y0, y1, z0, z1, shape_len=1)
     z_basis_state = circuit.final_state_vector(initial_state)
 
-    expected_state = np.zeros(2 ** 6)
+    expected_state = np.zeros(2**6)
     expected_state[0b010101] = 1
 
     cirq.testing.assert_allclose_up_to_global_phase(
@@ -618,7 +618,7 @@ def test_to_z_basis_ops_product_state():
     )
     z_basis_state = circuit.final_state_vector(initial_state)
 
-    expected_state = np.zeros(2 ** 6)
+    expected_state = np.zeros(2**6)
     expected_state[0b010101] = 1
 
     cirq.testing.assert_allclose_up_to_global_phase(
@@ -1320,8 +1320,8 @@ def test_pauli_string_expectation_from_density_matrix_pure_state_with_coef():
 def test_pauli_string_expectation_from_state_vector_mixed_state_linearity():
     n_qubits = 6
 
-    state_vector1 = cirq.testing.random_superposition(2 ** n_qubits)
-    state_vector2 = cirq.testing.random_superposition(2 ** n_qubits)
+    state_vector1 = cirq.testing.random_superposition(2**n_qubits)
+    state_vector2 = cirq.testing.random_superposition(2**n_qubits)
     rho1 = np.outer(state_vector1, np.conj(state_vector1))
     rho2 = np.outer(state_vector2, np.conj(state_vector2))
     density_matrix = rho1 / 2 + rho2 / 2
@@ -1390,7 +1390,7 @@ def test_conjugated_by_incorrectly_powered_cliffords():
     ]
     for c in cliffords:
         with pytest.raises(TypeError, match='not a known Clifford'):
-            _ = p.conjugated_by(c ** 0.1)
+            _ = p.conjugated_by(c**0.1)
         with pytest.raises(TypeError, match='not a known Clifford'):
             _ = p.conjugated_by(c ** sympy.Symbol('t'))
 
@@ -1444,24 +1444,12 @@ def _decompose_(self, qubits):
 def test_conjugated_by_move_into_uninvolved():
     a, b, c, d = cirq.LineQubit.range(4)
     p = cirq.X(a) * cirq.Z(b)
-    assert (
-        p.conjugated_by(
-            [
-                cirq.SWAP(c, d),
-                cirq.SWAP(b, c),
-            ]
-        )
-        == cirq.X(a) * cirq.Z(d)
-    )
-    assert (
-        p.conjugated_by(
-            [
-                cirq.SWAP(b, c),
-                cirq.SWAP(c, d),
-            ]
-        )
-        == cirq.X(a) * cirq.Z(c)
-    )
+    assert p.conjugated_by([cirq.SWAP(c, d), cirq.SWAP(b, c),]) == cirq.X(
+        a
+    ) * cirq.Z(d)
+    assert p.conjugated_by([cirq.SWAP(b, c), cirq.SWAP(c, d),]) == cirq.X(
+        a
+    ) * cirq.Z(c)
 
 
 def test_conjugated_by_common_single_qubit_gates():
@@ -1472,15 +1460,15 @@ def test_conjugated_by_common_single_qubit_gates():
         cirq.X,
         cirq.Y,
         cirq.Z,
-        cirq.X ** -0.5,
-        cirq.Y ** -0.5,
-        cirq.Z ** -0.5,
-        cirq.X ** 0.5,
-        cirq.Y ** 0.5,
-        cirq.Z ** 0.5,
+        cirq.X**-0.5,
+        cirq.Y**-0.5,
+        cirq.Z**-0.5,
+        cirq.X**0.5,
+        cirq.Y**0.5,
+        cirq.Z**0.5,
         cirq.H,
     ]
-    single_qubit_gates = [g ** i for i in range(4) for g in base_single_qubit_gates]
+    single_qubit_gates = [g**i for i in range(4) for g in base_single_qubit_gates]
     for p in [cirq.X, cirq.Y, cirq.Z]:
         for g in single_qubit_gates:
             assert p.on(a).conjugated_by(g.on(b)) == p.on(a)
@@ -1504,17 +1492,17 @@ def _decompose_(self, qubits):
         cirq.CNOT,
         cirq.CZ,
         cirq.ISWAP,
-        cirq.ISWAP ** -1,
+        cirq.ISWAP**-1,
         cirq.SWAP,
-        cirq.XX ** 0.5,
-        cirq.YY ** 0.5,
-        cirq.ZZ ** 0.5,
+        cirq.XX**0.5,
+        cirq.YY**0.5,
+        cirq.ZZ**0.5,
         cirq.XX,
         cirq.YY,
         cirq.ZZ,
-        cirq.XX ** -0.5,
-        cirq.YY ** -0.5,
-        cirq.ZZ ** -0.5,
+        cirq.XX**-0.5,
+        cirq.YY**-0.5,
+        cirq.ZZ**-0.5,
     ]
     two_qubit_gates.extend(
         [
@@ -1619,7 +1607,7 @@ def test_circuit_diagram_info():
             cirq.X(a) * cirq.Z(c),
             1j * cirq.X(a) * cirq.Y(b),
             -1j * cirq.Y(b),
-            1j ** 0.5 * cirq.X(a) * cirq.Y(b),
+            1j**0.5 * cirq.X(a) * cirq.Y(b),
         ),
         """
 0: ───PauliString(+X)───PauliString(-X)───PauliString(+X)───PauliString(iX)──────────────────────PauliString((0.707+0.707i)*X)───
@@ -1918,7 +1906,7 @@ def __rmul__(self, other):
 
 
 def test_coefficient_precision():
-    qs = cirq.LineQubit.range(4 * 10 ** 3)
+    qs = cirq.LineQubit.range(4 * 10**3)
     r = cirq.MutablePauliString({q: cirq.X for q in qs})
     r2 = cirq.MutablePauliString({q: cirq.Y for q in qs})
     r2 *= r
diff --git a/cirq/ops/pauli_sum_exponential_test.py b/cirq/ops/pauli_sum_exponential_test.py
index 8ea6b7b8cab..e9418e46d86 100644
--- a/cirq/ops/pauli_sum_exponential_test.py
+++ b/cirq/ops/pauli_sum_exponential_test.py
@@ -129,7 +129,7 @@ def test_pauli_sum_exponential_has_correct_unitary(psum_exp, expected_unitary):
     ),
 )
 def test_pauli_sum_exponential_pow(psum_exp, power, expected_psum):
-    assert psum_exp ** power == expected_psum
+    assert psum_exp**power == expected_psum
 
 
 @pytest.mark.parametrize(
diff --git a/cirq/ops/phased_iswap_gate_test.py b/cirq/ops/phased_iswap_gate_test.py
index 83f4ed1db22..4ee64f09671 100644
--- a/cirq/ops/phased_iswap_gate_test.py
+++ b/cirq/ops/phased_iswap_gate_test.py
@@ -31,7 +31,7 @@ def test_phased_iswap_init():
 
 
 def test_phased_iswap_equality():
-    assert cirq.PhasedISwapPowGate(phase_exponent=0, exponent=0.4) == cirq.ISWAP ** 0.4
+    assert cirq.PhasedISwapPowGate(phase_exponent=0, exponent=0.4) == cirq.ISWAP**0.4
 
 
 def test_repr():
@@ -82,7 +82,7 @@ def test_phased_iswap_str():
 def test_phased_iswap_pow():
     gate1 = cirq.PhasedISwapPowGate(phase_exponent=0.1, exponent=0.25)
     gate2 = cirq.PhasedISwapPowGate(phase_exponent=0.1, exponent=0.5)
-    assert gate1 ** 2 == gate2
+    assert gate1**2 == gate2
 
     u1 = cirq.unitary(gate1)
     u2 = cirq.unitary(gate2)
diff --git a/cirq/ops/phased_x_gate.py b/cirq/ops/phased_x_gate.py
index cf83219fbcd..ef17dfb583c 100644
--- a/cirq/ops/phased_x_gate.py
+++ b/cirq/ops/phased_x_gate.py
@@ -56,7 +56,7 @@ def _qasm_(self, args: 'cirq.QasmArgs', qubits: Tuple['cirq.Qid', ...]) -> Optio
 
         e = cast(float, value.canonicalize_half_turns(self._exponent))
         p = cast(float, self.phase_exponent)
-        epsilon = 10 ** -args.precision
+        epsilon = 10**-args.precision
 
         if abs(e + 0.5) <= epsilon:
             return args.format(
@@ -81,7 +81,7 @@ def _decompose_(self, qubits: Sequence['cirq.Qid']) -> 'cirq.OP_TREE':
         q = qubits[0]
         z = cirq.Z(q) ** self._phase_exponent
         x = cirq.XPowGate(exponent=self._exponent, global_shift=self.global_shift).on(q)
-        return z ** -1, x, z
+        return z**-1, x, z
 
     @property
     def exponent(self) -> Union[float, sympy.Symbol]:
@@ -119,8 +119,8 @@ def _unitary_(self) -> Union[np.ndarray, NotImplementedType]:
         """See `cirq.SupportsUnitary`."""
         if self._is_parameterized_():
             return None
-        z = protocols.unitary(cirq.Z ** self._phase_exponent)
-        x = protocols.unitary(cirq.X ** self._exponent)
+        z = protocols.unitary(cirq.Z**self._phase_exponent)
+        x = protocols.unitary(cirq.X**self._exponent)
         p = np.exp(1j * np.pi * self._global_shift * self._exponent)
         return np.dot(np.dot(z, x), np.conj(z)) * p
 
diff --git a/cirq/ops/phased_x_gate_test.py b/cirq/ops/phased_x_gate_test.py
index 04e8420cafd..c3fdfa1bc91 100644
--- a/cirq/ops/phased_x_gate_test.py
+++ b/cirq/ops/phased_x_gate_test.py
@@ -75,16 +75,16 @@ def test_no_symbolic_qasm_but_fails_gracefully(sym):
 
 def test_extrapolate():
     g = cirq.PhasedXPowGate(phase_exponent=0.25)
-    assert g ** 0.25 == (g ** 0.5) ** 0.5
+    assert g**0.25 == (g**0.5) ** 0.5
 
     # The gate is self-inverse, but there are hidden variables tracking the
     # exponent's sign and scale.
-    assert g ** -1 == g
+    assert g**-1 == g
     assert g.exponent == 1
-    assert (g ** -1).exponent == -1
-    assert g ** -0.5 == (g ** -1) ** 0.5 != g ** 0.5
-    assert g == g ** 3
-    assert g ** 0.5 != (g ** 3) ** 0.5 == g ** -0.5
+    assert (g**-1).exponent == -1
+    assert g**-0.5 == (g**-1) ** 0.5 != g**0.5
+    assert g == g**3
+    assert g**0.5 != (g**3) ** 0.5 == g**-0.5
 
 
 def test_eq():
@@ -104,7 +104,7 @@ def test_eq():
         cirq.PhasedXPowGate(phase_exponent=2.5, exponent=3),
         cirq.Y,
     )
-    eq.add_equality_group(cirq.PhasedXPowGate(phase_exponent=0.5, exponent=0.25), cirq.Y ** 0.25)
+    eq.add_equality_group(cirq.PhasedXPowGate(phase_exponent=0.5, exponent=0.25), cirq.Y**0.25)
 
     eq.add_equality_group(cirq.PhasedXPowGate(phase_exponent=0.25, exponent=0.25, global_shift=0.1))
     eq.add_equality_group(cirq.PhasedXPowGate(phase_exponent=2.25, exponent=0.25, global_shift=0.2))
diff --git a/cirq/ops/phased_x_z_gate.py b/cirq/ops/phased_x_z_gate.py
index d4bc1401e3a..053e3bffddb 100644
--- a/cirq/ops/phased_x_z_gate.py
+++ b/cirq/ops/phased_x_z_gate.py
@@ -145,8 +145,8 @@ def _unitary_(self) -> Optional[np.ndarray]:
         """See `cirq.SupportsUnitary`."""
         if self._is_parameterized_():
             return None
-        z_pre = protocols.unitary(ops.Z ** -self._axis_phase_exponent)
-        x = protocols.unitary(ops.X ** self._x_exponent)
+        z_pre = protocols.unitary(ops.Z**-self._axis_phase_exponent)
+        x = protocols.unitary(ops.X**self._x_exponent)
         z_post = protocols.unitary(ops.Z ** (self._axis_phase_exponent + self._z_exponent))
         return z_post @ x @ z_pre
 
diff --git a/cirq/ops/phased_x_z_gate_test.py b/cirq/ops/phased_x_z_gate_test.py
index 0536ff17984..cff85c1bc8e 100644
--- a/cirq/ops/phased_x_z_gate_test.py
+++ b/cirq/ops/phased_x_z_gate_test.py
@@ -124,32 +124,32 @@ def f(x, z, a):
 def test_from_matrix():
     # Axis rotations.
     assert cirq.approx_eq(
-        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.X ** 0.1)),
+        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.X**0.1)),
         cirq.PhasedXZGate(x_exponent=0.1, z_exponent=0, axis_phase_exponent=0),
         atol=1e-8,
     )
     assert cirq.approx_eq(
-        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.X ** -0.1)),
+        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.X**-0.1)),
         cirq.PhasedXZGate(x_exponent=-0.1, z_exponent=0, axis_phase_exponent=0),
         atol=1e-8,
     )
     assert cirq.approx_eq(
-        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.Y ** 0.1)),
+        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.Y**0.1)),
         cirq.PhasedXZGate(x_exponent=0.1, z_exponent=0, axis_phase_exponent=0.5),
         atol=1e-8,
     )
     assert cirq.approx_eq(
-        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.Y ** -0.1)),
+        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.Y**-0.1)),
         cirq.PhasedXZGate(x_exponent=-0.1, z_exponent=0, axis_phase_exponent=0.5),
         atol=1e-8,
     )
     assert cirq.approx_eq(
-        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.Z ** -0.1)),
+        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.Z**-0.1)),
         cirq.PhasedXZGate(x_exponent=0, z_exponent=-0.1, axis_phase_exponent=0),
         atol=1e-8,
     )
     assert cirq.approx_eq(
-        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.Z ** 0.1)),
+        cirq.PhasedXZGate.from_matrix(cirq.unitary(cirq.Z**0.1)),
         cirq.PhasedXZGate(x_exponent=0, z_exponent=0.1, axis_phase_exponent=0),
         atol=1e-8,
     )
@@ -240,7 +240,7 @@ def test_inverse():
     g = cirq.PhasedXZGate(x_exponent=a, z_exponent=b, axis_phase_exponent=c).on(q)
 
     cirq.testing.assert_allclose_up_to_global_phase(
-        cirq.unitary(g ** -1), np.transpose(np.conjugate(cirq.unitary(g))), atol=1e-8
+        cirq.unitary(g**-1), np.transpose(np.conjugate(cirq.unitary(g))), atol=1e-8
     )
 
 
diff --git a/cirq/ops/raw_types.py b/cirq/ops/raw_types.py
index 56299bc60f2..b1074306440 100644
--- a/cirq/ops/raw_types.py
+++ b/cirq/ops/raw_types.py
@@ -598,7 +598,7 @@ def _commutes_(
 
         # Don't create gigantic matrices.
         shape = protocols.qid_shape_protocol.qid_shape(circuit12)
-        if np.prod(shape, dtype=np.int64) > 2 ** 10:
+        if np.prod(shape, dtype=np.int64) > 2**10:
             return NotImplemented  # coverage: ignore
 
         m12 = protocols.unitary_protocol.unitary(circuit12, default=None)
@@ -841,7 +841,7 @@ def _phase_by_(self, phase_turns: float, qubit_index: int) -> 'cirq.Operation':
         return protocols.phase_by(self.sub_operation, phase_turns, qubit_index)
 
     def __pow__(self, exponent: Any) -> 'cirq.Operation':
-        return self.sub_operation ** exponent
+        return self.sub_operation**exponent
 
     def __mul__(self, other: Any) -> Any:
         return self.sub_operation * other
diff --git a/cirq/ops/raw_types_test.py b/cirq/ops/raw_types_test.py
index d27433f8547..15c6c2a1def 100644
--- a/cirq/ops/raw_types_test.py
+++ b/cirq/ops/raw_types_test.py
@@ -171,9 +171,9 @@ def __repr__(self):
         TestGate().on(a)
 
     t = TestGate().on(a, b)
-    i = t ** -1
-    assert i ** -1 == t
-    assert t ** -1 == i
+    i = t**-1
+    assert i**-1 == t
+    assert t**-1 == i
     assert cirq.decompose(i) == [cirq.X(a), cirq.S(b) ** -1, cirq.Z(a)]
     cirq.testing.assert_allclose_up_to_global_phase(
         cirq.unitary(i), cirq.unitary(t).conj().T, atol=1e-8
@@ -188,7 +188,7 @@ def _num_qubits_(self):
             return 3
 
         def _decompose_(self, qubits):
-            return (cirq.X ** 0.1).on_each(*qubits)
+            return (cirq.X**0.1).on_each(*qubits)
 
     assert cirq.inverse(TestGate(), None) is not None
     cirq.testing.assert_has_consistent_qid_shape(cirq.inverse(TestGate()))
@@ -214,7 +214,7 @@ def _qid_shape_(self):
             return (1, 2, 3)
 
         def _decompose_(self, qubits):
-            return (cirq.X ** 0.1).on(qubits[1])
+            return (cirq.X**0.1).on(qubits[1])
 
     assert cirq.qid_shape(cirq.inverse(TestGate(), None)) == (1, 2, 3)
     cirq.testing.assert_has_consistent_qid_shape(cirq.inverse(TestGate()))
@@ -616,7 +616,7 @@ def test_tagged_operation_forwards_protocols():
 
     y = cirq.Y(q1)
     tagged_y = cirq.Y(q1).with_tags(tag)
-    assert tagged_y ** 0.5 == cirq.YPowGate(exponent=0.5)(q1)
+    assert tagged_y**0.5 == cirq.YPowGate(exponent=0.5)(q1)
     assert tagged_y * 2 == (y * 2)
     assert 3 * tagged_y == (3 * y)
     assert cirq.phase_by(y, 0.125, 0) == cirq.phase_by(tagged_y, 0.125, 0)
@@ -635,8 +635,8 @@ def test_tagged_operation_forwards_protocols():
     assert cirq.commutes(clifford_x, tagged_x)
     assert cirq.commutes(tagged_x, tagged_x)
 
-    assert cirq.trace_distance_bound(y ** 0.001) == cirq.trace_distance_bound(
-        (y ** 0.001).with_tags(tag)
+    assert cirq.trace_distance_bound(y**0.001) == cirq.trace_distance_bound(
+        (y**0.001).with_tags(tag)
     )
 
     flip = cirq.bit_flip(0.5)(q1)
diff --git a/cirq/ops/state_preparation_channel.py b/cirq/ops/state_preparation_channel.py
index 3c1bcab0b5d..daf6b0faca7 100644
--- a/cirq/ops/state_preparation_channel.py
+++ b/cirq/ops/state_preparation_channel.py
@@ -43,7 +43,7 @@ def __init__(self, target_state: np.ndarray, *, name: str = "StatePreparation")
             raise ValueError('`target_state` must be a 1d numpy array.')
 
         n = int(np.round(np.log2(target_state.shape[0] or 1)))
-        if 2 ** n != target_state.shape[0]:
+        if 2**n != target_state.shape[0]:
             raise ValueError(f'Matrix width ({target_state.shape[0]}) is not a power of 2')
 
         self._state = target_state.astype(np.complex128) / np.linalg.norm(target_state)
@@ -104,7 +104,7 @@ def _kraus_(self) -> Iterable[np.ndarray]:
         This allows is to take any input state to the target state.
         The operator satisfies the completeness relation Sum(E^ E) = I.
         """
-        operator = np.zeros(shape=(2 ** self._num_qubits,) * 3, dtype=np.complex128)
+        operator = np.zeros(shape=(2**self._num_qubits,) * 3, dtype=np.complex128)
         for i in range(len(operator)):
             operator[i, :, i] = self._state
         return operator
diff --git a/cirq/ops/swap_gates.py b/cirq/ops/swap_gates.py
index d0b556a23ca..72b9a1c41ba 100644
--- a/cirq/ops/swap_gates.py
+++ b/cirq/ops/swap_gates.py
@@ -112,7 +112,7 @@ def _pauli_expansion_(self) -> value.LinearDict[str]:
         if protocols.is_parameterized(self):
             return NotImplemented
         global_phase = 1j ** (2 * self._exponent * self._global_shift)
-        swap_phase = 1j ** self._exponent
+        swap_phase = 1j**self._exponent
         c = -1j * swap_phase * np.sin(np.pi * self._exponent / 2) / 2
         return value.LinearDict(
             {
diff --git a/cirq/ops/swap_gates_test.py b/cirq/ops/swap_gates_test.py
index 2cdf003693a..17fd161b17b 100644
--- a/cirq/ops/swap_gates_test.py
+++ b/cirq/ops/swap_gates_test.py
@@ -77,8 +77,8 @@ def test_text_diagrams():
 
 def test_swap_has_stabilizer_effect():
     assert cirq.has_stabilizer_effect(cirq.SWAP)
-    assert cirq.has_stabilizer_effect(cirq.SWAP ** 2)
-    assert not cirq.has_stabilizer_effect(cirq.SWAP ** 0.5)
+    assert cirq.has_stabilizer_effect(cirq.SWAP**2)
+    assert not cirq.has_stabilizer_effect(cirq.SWAP**0.5)
     assert not cirq.has_stabilizer_effect(cirq.SWAP ** sympy.Symbol('foo'))
 
 
@@ -139,18 +139,18 @@ def test_sqrt_iswap_inv_unitary():
 
 def test_repr():
     assert repr(cirq.SWAP) == 'cirq.SWAP'
-    assert repr(cirq.SWAP ** 0.5) == '(cirq.SWAP**0.5)'
+    assert repr(cirq.SWAP**0.5) == '(cirq.SWAP**0.5)'
 
     assert repr(cirq.ISWAP) == 'cirq.ISWAP'
-    assert repr(cirq.ISWAP ** 0.5) == '(cirq.ISWAP**0.5)'
+    assert repr(cirq.ISWAP**0.5) == '(cirq.ISWAP**0.5)'
 
 
 def test_str():
     assert str(cirq.SWAP) == 'SWAP'
-    assert str(cirq.SWAP ** 0.5) == 'SWAP**0.5'
+    assert str(cirq.SWAP**0.5) == 'SWAP**0.5'
 
     assert str(cirq.ISWAP) == 'ISWAP'
-    assert str(cirq.ISWAP ** 0.5) == 'ISWAP**0.5'
+    assert str(cirq.ISWAP**0.5) == 'ISWAP**0.5'
 
 
 def test_iswap_decompose_diagram():
@@ -170,20 +170,20 @@ def test_iswap_decompose_diagram():
 
 def test_trace_distance():
     foo = sympy.Symbol('foo')
-    sswap = cirq.SWAP ** foo
-    siswap = cirq.ISWAP ** foo
+    sswap = cirq.SWAP**foo
+    siswap = cirq.ISWAP**foo
     # These values should have 1.0 or 0.0 directly returned
     assert cirq.trace_distance_bound(sswap) == 1.0
     assert cirq.trace_distance_bound(siswap) == 1.0
     # These values are calculated, so we use approx_eq
-    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.SWAP ** 0.3), np.sin(0.3 * np.pi / 2))
-    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.ISWAP ** 0), 0.0)
+    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.SWAP**0.3), np.sin(0.3 * np.pi / 2))
+    assert cirq.approx_eq(cirq.trace_distance_bound(cirq.ISWAP**0), 0.0)
 
 
 def test_trace_distance_over_range_of_exponents():
     for exp in np.linspace(0, 4, 20):
-        cirq.testing.assert_has_consistent_trace_distance_bound(cirq.SWAP ** exp)
-        cirq.testing.assert_has_consistent_trace_distance_bound(cirq.ISWAP ** exp)
+        cirq.testing.assert_has_consistent_trace_distance_bound(cirq.SWAP**exp)
+        cirq.testing.assert_has_consistent_trace_distance_bound(cirq.ISWAP**exp)
 
 
 @pytest.mark.parametrize('angle_rads', (-np.pi, -np.pi / 3, -0.1, np.pi / 5))
diff --git a/cirq/ops/three_qubit_gates.py b/cirq/ops/three_qubit_gates.py
index 25e583f1f73..d32b161547b 100644
--- a/cirq/ops/three_qubit_gates.py
+++ b/cirq/ops/three_qubit_gates.py
@@ -69,7 +69,7 @@ def _pauli_expansion_(self) -> value.LinearDict[str]:
         if protocols.is_parameterized(self):
             return NotImplemented
         global_phase = 1j ** (2 * self._exponent * self._global_shift)
-        z_phase = 1j ** self._exponent
+        z_phase = 1j**self._exponent
         c = -1j * z_phase * np.sin(np.pi * self._exponent / 2) / 4
         return value.LinearDict(
             {
@@ -104,7 +104,7 @@ def _decompose_(self, qubits):
             elif not b.is_adjacent(c):
                 a, b = b, a
 
-        p = common_gates.T ** self._exponent
+        p = common_gates.T**self._exponent
         sweep_abc = [common_gates.CNOT(a, b), common_gates.CNOT(b, c)]
 
         return [
@@ -389,7 +389,7 @@ def _pauli_expansion_(self) -> value.LinearDict[str]:
         if protocols.is_parameterized(self):
             return NotImplemented
         global_phase = 1j ** (2 * self._exponent * self._global_shift)
-        z_phase = 1j ** self._exponent
+        z_phase = 1j**self._exponent
         c = -1j * z_phase * np.sin(np.pi * self._exponent / 2) / 4
         return value.LinearDict(
             {
@@ -415,7 +415,7 @@ def _apply_unitary_(self, args: 'protocols.ApplyUnitaryArgs') -> np.ndarray:
             args.target_tensor *= p
         return protocols.apply_unitary(
             controlled_gate.ControlledGate(
-                controlled_gate.ControlledGate(pauli_gates.X ** self.exponent)
+                controlled_gate.ControlledGate(pauli_gates.X**self.exponent)
             ),
             protocols.ApplyUnitaryArgs(args.target_tensor, args.available_buffer, args.axes),
             default=NotImplemented,
diff --git a/cirq/ops/three_qubit_gates_test.py b/cirq/ops/three_qubit_gates_test.py
index bf9e3f4b7f4..77ecabcbb91 100644
--- a/cirq/ops/three_qubit_gates_test.py
+++ b/cirq/ops/three_qubit_gates_test.py
@@ -50,10 +50,10 @@ def test_consistent_protocols(gate, ignoring_global_phase):
 
 
 def test_init():
-    assert (cirq.CCZ ** 0.5).exponent == 0.5
-    assert (cirq.CCZ ** 0.25).exponent == 0.25
-    assert (cirq.CCX ** 0.5).exponent == 0.5
-    assert (cirq.CCX ** 0.25).exponent == 0.25
+    assert (cirq.CCZ**0.5).exponent == 0.5
+    assert (cirq.CCZ**0.25).exponent == 0.25
+    assert (cirq.CCX**0.5).exponent == 0.5
+    assert (cirq.CCX**0.25).exponent == 0.25
 
 
 def test_unitary():
@@ -75,9 +75,9 @@ def test_unitary():
         atol=1e-8,
     )
 
-    assert cirq.has_unitary(cirq.CCX ** 0.5)
+    assert cirq.has_unitary(cirq.CCX**0.5)
     np.testing.assert_allclose(
-        cirq.unitary(cirq.CCX ** 0.5),
+        cirq.unitary(cirq.CCX**0.5),
         np.array(
             [
                 [1, 0, 0, 0, 0, 0, 0, 0],
@@ -98,9 +98,9 @@ def test_unitary():
         cirq.unitary(cirq.CCZ), np.diag([1, 1, 1, 1, 1, 1, 1, -1]), atol=1e-8
     )
 
-    assert cirq.has_unitary(cirq.CCZ ** 0.5)
+    assert cirq.has_unitary(cirq.CCZ**0.5)
     np.testing.assert_allclose(
-        cirq.unitary(cirq.CCZ ** 0.5), np.diag([1, 1, 1, 1, 1, 1, 1, 1j]), atol=1e-8
+        cirq.unitary(cirq.CCZ**0.5), np.diag([1, 1, 1, 1, 1, 1, 1, 1j]), atol=1e-8
     )
 
     assert cirq.has_unitary(cirq.CSWAP)
@@ -137,8 +137,8 @@ def test_str():
     assert str(cirq.FREDKIN) == 'FREDKIN'
     assert str(cirq.CCZ) == 'CCZ'
 
-    assert str(cirq.CCX ** 0.5) == 'TOFFOLI**0.5'
-    assert str(cirq.CCZ ** 0.5) == 'CCZ**0.5'
+    assert str(cirq.CCX**0.5) == 'TOFFOLI**0.5'
+    assert str(cirq.CCZ**0.5) == 'CCZ**0.5'
 
 
 def test_repr():
@@ -148,8 +148,8 @@ def test_repr():
     assert repr(cirq.FREDKIN) == 'cirq.FREDKIN'
     assert repr(cirq.CCZ) == 'cirq.CCZ'
 
-    assert repr(cirq.CCX ** 0.5) == '(cirq.TOFFOLI**0.5)'
-    assert repr(cirq.CCZ ** 0.5) == '(cirq.CCZ**0.5)'
+    assert repr(cirq.CCX**0.5) == '(cirq.TOFFOLI**0.5)'
+    assert repr(cirq.CCZ**0.5) == '(cirq.CCZ**0.5)'
 
 
 def test_eq():
@@ -300,7 +300,7 @@ def test_diagonal_exponent():
     diagonal_angles = [2, 3, 5, 7, 11, 13, 17, 19]
     diagonal_gate = cirq.ThreeQubitDiagonalGate(diagonal_angles)
 
-    sqrt_diagonal_gate = diagonal_gate ** 0.5
+    sqrt_diagonal_gate = diagonal_gate**0.5
 
     expected_angles = [prime / 2 for prime in diagonal_angles]
     np.testing.assert_allclose(expected_angles, sqrt_diagonal_gate._diag_angles_radians, atol=1e-8)
diff --git a/cirq/ops/two_qubit_diagonal_gate_test.py b/cirq/ops/two_qubit_diagonal_gate_test.py
index 966729b01f9..f72550174de 100644
--- a/cirq/ops/two_qubit_diagonal_gate_test.py
+++ b/cirq/ops/two_qubit_diagonal_gate_test.py
@@ -87,7 +87,7 @@ def test_diagonal_exponent():
     diagonal_angles = [2, 3, 5, 7]
     diagonal_gate = cirq.TwoQubitDiagonalGate(diagonal_angles)
 
-    sqrt_diagonal_gate = diagonal_gate ** 0.5
+    sqrt_diagonal_gate = diagonal_gate**0.5
 
     expected_angles = [prime / 2 for prime in diagonal_angles]
     assert cirq.approx_eq(sqrt_diagonal_gate, cirq.TwoQubitDiagonalGate(expected_angles))
diff --git a/cirq/optimizers/merge_interactions_test.py b/cirq/optimizers/merge_interactions_test.py
index d508c50a5fd..8df5bcf561c 100644
--- a/cirq/optimizers/merge_interactions_test.py
+++ b/cirq/optimizers/merge_interactions_test.py
@@ -174,7 +174,7 @@ def test_optimizes_single_iswap():
 
 def test_optimizes_tagged_partial_cz():
     a, b = cirq.LineQubit.range(2)
-    c = cirq.Circuit((cirq.CZ ** 0.5)(a, b).with_tags('mytag'))
+    c = cirq.Circuit((cirq.CZ**0.5)(a, b).with_tags('mytag'))
     assert_optimization_not_broken(c)
     with cirq.testing.assert_deprecated(
         "Use cirq.optimize_for_target_gateset", deadline='v1.0', count=2
diff --git a/cirq/optimizers/merge_single_qubit_gates_test.py b/cirq/optimizers/merge_single_qubit_gates_test.py
index 2a43b1c4377..805965c16d3 100644
--- a/cirq/optimizers/merge_single_qubit_gates_test.py
+++ b/cirq/optimizers/merge_single_qubit_gates_test.py
@@ -70,7 +70,7 @@ def test_combines_sequence():
     assert len(opt_summary.new_operations) == 1
     assert isinstance(opt_summary.new_operations[0].gate, cirq.MatrixGate)
     cirq.testing.assert_allclose_up_to_global_phase(
-        cirq.unitary(opt_summary.new_operations[0]), cirq.unitary(cirq.Y ** 0.5), atol=1e-7
+        cirq.unitary(opt_summary.new_operations[0]), cirq.unitary(cirq.Y**0.5), atol=1e-7
     )
 
 
diff --git a/cirq/protocols/circuit_diagram_info_protocol.py b/cirq/protocols/circuit_diagram_info_protocol.py
index 61ae35661ea..9718617a6c7 100644
--- a/cirq/protocols/circuit_diagram_info_protocol.py
+++ b/cirq/protocols/circuit_diagram_info_protocol.py
@@ -146,7 +146,7 @@ def _formatted_exponent(
                 # funky behavior of fraction, cast to str in constructor helps.
                 approx_frac = Fraction(self.exponent).limit_denominator(16)
                 if approx_frac.denominator not in [2, 4, 5, 10]:
-                    if abs(float(approx_frac) - self.exponent) < 10 ** -args.precision:
+                    if abs(float(approx_frac) - self.exponent) < 10**-args.precision:
                         return f'({approx_frac})'
 
                 return args.format_real(self.exponent)
diff --git a/cirq/protocols/json_serialization_test.py b/cirq/protocols/json_serialization_test.py
index c69a0a017d0..c1c5eb6d2e8 100644
--- a/cirq/protocols/json_serialization_test.py
+++ b/cirq/protocols/json_serialization_test.py
@@ -412,7 +412,7 @@ def test_sympy():
     assert_json_roundtrip_works(t * s)
     assert_json_roundtrip_works(t / s)
     assert_json_roundtrip_works(t - s)
-    assert_json_roundtrip_works(t ** s)
+    assert_json_roundtrip_works(t**s)
 
     # Linear combinations.
     assert_json_roundtrip_works(t * 2)
diff --git a/cirq/protocols/pow_protocol_test.py b/cirq/protocols/pow_protocol_test.py
index bce9ddd5389..12185ee003b 100644
--- a/cirq/protocols/pow_protocol_test.py
+++ b/cirq/protocols/pow_protocol_test.py
@@ -65,5 +65,5 @@ def test_pow_error():
 )
 def test_pow_with_result(val, exponent, out):
     assert (
-        cirq.pow(val, exponent) == cirq.pow(val, exponent, default=None) == val ** exponent == out
+        cirq.pow(val, exponent) == cirq.pow(val, exponent, default=None) == val**exponent == out
     )
diff --git a/cirq/protocols/qid_shape_protocol.py b/cirq/protocols/qid_shape_protocol.py
index fa145b17149..bb300496616 100644
--- a/cirq/protocols/qid_shape_protocol.py
+++ b/cirq/protocols/qid_shape_protocol.py
@@ -27,7 +27,7 @@
 # user provides a different (0,) value.
 RaiseTypeErrorIfNotProvided: Any = (0,)
 # Equal integers outside the range [-5, 256] aren't identically equal with `is`.
-RaiseTypeErrorIfNotProvidedInt: Any = -(2 ** 512)
+RaiseTypeErrorIfNotProvidedInt: Any = -(2**512)
 
 TDefault = TypeVar('TDefault')
 
diff --git a/cirq/protocols/trace_distance_bound.py b/cirq/protocols/trace_distance_bound.py
index 8e833e78c61..69cd6ee89cf 100644
--- a/cirq/protocols/trace_distance_bound.py
+++ b/cirq/protocols/trace_distance_bound.py
@@ -104,7 +104,7 @@ def _strat_distance_from_unitary(val: Any) -> Optional[float]:
         squared = 1 - (0.5 * abs(u[0][0] + u[1][1])) ** 2
         if squared <= 0:
             return 0.0
-        return squared ** 0.5
+        return squared**0.5
 
     return trace_distance_from_angle_list(np.angle(np.linalg.eigvals(u)))
 
diff --git a/cirq/protocols/trace_distance_bound_test.py b/cirq/protocols/trace_distance_bound_test.py
index 73b7a9e2832..0a7aa2ccc69 100644
--- a/cirq/protocols/trace_distance_bound_test.py
+++ b/cirq/protocols/trace_distance_bound_test.py
@@ -37,11 +37,11 @@ def _trace_distance_bound_(self) -> float:
 
     x = cirq.MatrixGate(cirq.unitary(cirq.X))
     cx = cirq.MatrixGate(cirq.unitary(cirq.CX))
-    cxh = cirq.MatrixGate(cirq.unitary(cirq.CX ** 0.5))
+    cxh = cirq.MatrixGate(cirq.unitary(cirq.CX**0.5))
 
     assert np.isclose(cirq.trace_distance_bound(x), cirq.trace_distance_bound(cirq.X))
     assert np.isclose(cirq.trace_distance_bound(cx), cirq.trace_distance_bound(cirq.CX))
-    assert np.isclose(cirq.trace_distance_bound(cxh), cirq.trace_distance_bound(cirq.CX ** 0.5))
+    assert np.isclose(cirq.trace_distance_bound(cxh), cirq.trace_distance_bound(cirq.CX**0.5))
     assert cirq.trace_distance_bound(NoMethod()) == 1.0
     assert cirq.trace_distance_bound(ReturnsNotImplemented()) == 1.0
     assert cirq.trace_distance_bound(ReturnsTwo()) == 1.0
diff --git a/cirq/qis/channels_test.py b/cirq/qis/channels_test.py
index 28ccab03540..6856684be9e 100644
--- a/cirq/qis/channels_test.py
+++ b/cirq/qis/channels_test.py
@@ -252,7 +252,7 @@ def test_operation_to_choi(channel):
     n_qubits = cirq.num_qubits(channel)
     actual = cirq.operation_to_choi(channel)
     expected = compute_choi(channel)
-    assert np.isclose(np.trace(actual), 2 ** n_qubits)
+    assert np.isclose(np.trace(actual), 2**n_qubits)
     assert np.all(actual == expected)
 
 
diff --git a/cirq/qis/clifford_tableau_test.py b/cirq/qis/clifford_tableau_test.py
index 06f7aba3120..b8d5add1d47 100644
--- a/cirq/qis/clifford_tableau_test.py
+++ b/cirq/qis/clifford_tableau_test.py
@@ -45,7 +45,7 @@ def _CNOT(table, q1, q2):
 
 @pytest.mark.parametrize('num_qubits', range(1, 4))
 def test_tableau_initial_state_string(num_qubits):
-    for i in range(2 ** num_qubits):
+    for i in range(2**num_qubits):
         t = cirq.CliffordTableau(initial_state=i, num_qubits=num_qubits)
         splitted_represent_string = str(t).split('\n')
         assert len(splitted_represent_string) == num_qubits
@@ -179,7 +179,7 @@ def test_measurement():
 
 def test_validate_tableau():
     num_qubits = 4
-    for i in range(2 ** num_qubits):
+    for i in range(2**num_qubits):
         t = cirq.CliffordTableau(initial_state=i, num_qubits=num_qubits)
         assert t._validate()
 
diff --git a/cirq/qis/measures.py b/cirq/qis/measures.py
index 38602bca319..06da5f8cb13 100644
--- a/cirq/qis/measures.py
+++ b/cirq/qis/measures.py
@@ -120,7 +120,7 @@ def fidelity(
         for q, s1 in state1:
             s2 = state2[q]
             prod *= np.abs(np.vdot(s1.state_vector(), s2.state_vector()))
-        return prod ** 2
+        return prod**2
 
     # Two numpy arrays that are either state vector, state tensor, or
     # density matrix
@@ -244,7 +244,7 @@ def _fidelity_state_vectors_or_density_matrices(state1: np.ndarray, state2: np.n
         state1_sqrt = _sqrt_positive_semidefinite_matrix(state1)
         eigs = linalg.eigvalsh(state1_sqrt @ state2 @ state1_sqrt)
         trace = np.sum(np.sqrt(np.abs(eigs)))
-        return trace ** 2
+        return trace**2
     raise ValueError(
         'The given arrays must be one- or two-dimensional. '
         f'Got shapes {state1.shape} and {state2.shape}.'
@@ -310,4 +310,4 @@ def entanglement_fidelity(operation: 'cirq.SupportsKraus') -> float:
     for k in protocols.kraus(operation):
         f += np.abs(np.trace(k)) ** 2
     n_qubits = protocols.num_qubits(operation)
-    return float(f / 4 ** n_qubits)
+    return float(f / 4**n_qubits)
diff --git a/cirq/qis/states_test.py b/cirq/qis/states_test.py
index 5088b887e82..518fd51ec48 100644
--- a/cirq/qis/states_test.py
+++ b/cirq/qis/states_test.py
@@ -198,37 +198,28 @@ def test_infer_qid_shape():
     q0, q1 = cirq.LineQubit.range(2)
     product_state_1 = cirq.KET_PLUS(q0) * cirq.KET_PLUS(q1)
 
-    assert (
-        cirq.qis.infer_qid_shape(
-            computational_basis_state_1,
-            state_vector_1,
-            state_tensor_1,
-            density_matrix_1,
-            product_state_1,
-        )
-        == (2, 2)
-    )
+    assert cirq.qis.infer_qid_shape(
+        computational_basis_state_1,
+        state_vector_1,
+        state_tensor_1,
+        density_matrix_1,
+        product_state_1,
+    ) == (2, 2)
 
-    assert (
-        cirq.qis.infer_qid_shape(
-            product_state_1,
-            density_matrix_1,
-            state_tensor_1,
-            state_vector_1,
-            computational_basis_state_1,
-        )
-        == (2, 2)
-    )
+    assert cirq.qis.infer_qid_shape(
+        product_state_1,
+        density_matrix_1,
+        state_tensor_1,
+        state_vector_1,
+        computational_basis_state_1,
+    ) == (2, 2)
 
-    assert (
-        cirq.qis.infer_qid_shape(
-            computational_basis_state_1,
-            computational_basis_state_2,
-            computational_basis_state_4,
-            state_tensor_2,
-        )
-        == (1, 2, 3, 4)
-    )
+    assert cirq.qis.infer_qid_shape(
+        computational_basis_state_1,
+        computational_basis_state_2,
+        computational_basis_state_4,
+        state_tensor_2,
+    ) == (1, 2, 3, 4)
 
     assert cirq.qis.infer_qid_shape(
         state_vector_2, density_matrix_2, computational_basis_state_4
@@ -499,7 +490,7 @@ def test_to_valid_state_vector():
     np.testing.assert_almost_equal(cirq.to_valid_state_vector(1, 2), np.array([0.0, 1.0, 0.0, 0.0]))
 
     v = cirq.to_valid_state_vector([0, 1, 2, 0], qid_shape=(3, 3, 3, 3))
-    assert v.shape == (3 ** 4,)
+    assert v.shape == (3**4,)
     assert v[6 + 9] == 1
 
     v = cirq.to_valid_state_vector([False, True, False, False], num_qubits=4)
diff --git a/cirq/sim/clifford/act_on_stabilizer_ch_form_args_test.py b/cirq/sim/clifford/act_on_stabilizer_ch_form_args_test.py
index 13133a0b44e..7c9629427a3 100644
--- a/cirq/sim/clifford/act_on_stabilizer_ch_form_args_test.py
+++ b/cirq/sim/clifford/act_on_stabilizer_ch_form_args_test.py
@@ -95,7 +95,7 @@ def num_qubits(self) -> int:
             return 1
 
         def _unitary_(self):
-            return np.array([[1, 1], [1, -1]]) / (2 ** 0.5)
+            return np.array([[1, 1], [1, -1]]) / (2**0.5)
 
     args = cirq.ActOnStabilizerCHFormArgs(
         qubits=cirq.LineQubit.range(3),
diff --git a/cirq/sim/clifford/stabilizer_state_ch_form.py b/cirq/sim/clifford/stabilizer_state_ch_form.py
index ad6c3c63945..3f2827b6359 100644
--- a/cirq/sim/clifford/stabilizer_state_ch_form.py
+++ b/cirq/sim/clifford/stabilizer_state_ch_form.py
@@ -117,15 +117,15 @@ def inner_product_of_state_and_x(self, x: int) -> Union[float, complex]:
         return (
             self.omega
             * 2 ** (-sum(self.v) / 2)
-            * 1j ** mu
+            * 1j**mu
             * (-1) ** sum(self.v & u & self.s)
             * np.all(self.v | (u == self.s))
         )
 
     def state_vector(self) -> np.ndarray:
-        wf = np.zeros(2 ** self.n, dtype=complex)
+        wf = np.zeros(2**self.n, dtype=complex)
 
-        for x in range(2 ** self.n):
+        for x in range(2**self.n):
             wf[x] = self.inner_product_of_state_and_x(x)
 
         return wf
@@ -154,7 +154,7 @@ def update_sum(self, t, u, delta=0, alpha=0):
         """
         if np.all(t == u):
             self.s = t
-            self.omega *= 1 / np.sqrt(2) * (-1) ** alpha * (1 + 1j ** delta)
+            self.omega *= 1 / np.sqrt(2) * (-1) ** alpha * (1 + 1j**delta)
             return
         set0 = np.where((~self.v) & (t ^ u))[0]
         set1 = np.where(self.v & (t ^ u))[0]
@@ -221,7 +221,7 @@ def _H_decompose(self, v, y, z, delta):
                 c = bool(delta >> 1)
                 omega = (-1) ** (c & y)
             else:
-                omega = 1 / np.sqrt(2) * (1 + 1j ** delta)
+                omega = 1 / np.sqrt(2) * (1 + 1j**delta)
                 b = True
                 a = True
                 c = not ((delta >> 1) ^ y)
@@ -229,7 +229,7 @@ def _H_decompose(self, v, y, z, delta):
         return omega, a, b, c
 
     def to_state_vector(self) -> np.ndarray:
-        arr = np.zeros(2 ** self.n, dtype=complex)
+        arr = np.zeros(2**self.n, dtype=complex)
 
         for x in range(len(arr)):
             arr[x] = self.inner_product_of_state_and_x(x)
@@ -310,7 +310,7 @@ def apply_y(self, axis: int, exponent: float = 1, global_shift: float = 0):
         elif exponent % 2 == 0.5:
             self.apply_z(axis)
             self.apply_h(axis)
-            self.omega *= shift * (1 + 1j) / (2 ** 0.5)
+            self.omega *= shift * (1 + 1j) / (2**0.5)
         elif exponent % 2 == 1:
             self.apply_z(axis)
             self.apply_h(axis)
@@ -320,7 +320,7 @@ def apply_y(self, axis: int, exponent: float = 1, global_shift: float = 0):
         elif exponent % 2 == 1.5:
             self.apply_h(axis)
             self.apply_z(axis)
-            self.omega *= shift * (1 - 1j) / (2 ** 0.5)
+            self.omega *= shift * (1 - 1j) / (2**0.5)
 
     def apply_z(self, axis: int, exponent: float = 1, global_shift: float = 0):
         if exponent % 2 != 0:
diff --git a/cirq/sim/density_matrix_simulator_test.py b/cirq/sim/density_matrix_simulator_test.py
index 86aa6d1ae65..da0a6d7c425 100644
--- a/cirq/sim/density_matrix_simulator_test.py
+++ b/cirq/sim/density_matrix_simulator_test.py
@@ -121,7 +121,7 @@ def test_run_bit_flips(dtype: Type[np.number], split: bool):
     for b0 in [0, 1]:
         for b1 in [0, 1]:
             circuit = cirq.Circuit(
-                (cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0), cirq.measure(q1)
+                (cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0), cirq.measure(q1)
             )
             result = simulator.run(circuit)
             np.testing.assert_equal(result.measurements, {'0': [[b0]], '1': [[b1]]})
@@ -135,7 +135,7 @@ def test_run_bit_flips_with_dephasing(dtype: Type[np.number], split: bool):
     for b0 in [0, 1]:
         for b1 in [0, 1]:
             circuit = cirq.Circuit(
-                (cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0), cirq.measure(q1)
+                (cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0), cirq.measure(q1)
             )
             result = simulator.run(circuit)
             np.testing.assert_equal(result.measurements, {'0': [[b0]], '1': [[b1]]})
@@ -261,9 +261,9 @@ def _qid_shape_(self):
 
         def _kraus_(self):
             return [
-                np.array([[1, 0, 0], [0, 0.5 ** 0.5, 0], [0, 0, 0.5 ** 0.5]]),
-                np.array([[0, 0.5 ** 0.5, 0], [0, 0, 0], [0, 0, 0]]),
-                np.array([[0, 0, 0], [0, 0, 0.5 ** 0.5], [0, 0, 0]]),
+                np.array([[1, 0, 0], [0, 0.5**0.5, 0], [0, 0, 0.5**0.5]]),
+                np.array([[0, 0.5**0.5, 0], [0, 0, 0], [0, 0, 0]]),
+                np.array([[0, 0, 0], [0, 0, 0.5**0.5], [0, 0, 0]]),
             ]
 
     q0, q1 = cirq.LineQid.for_qid_shape((3, 4))
@@ -293,7 +293,7 @@ def test_run_measure_at_end_no_repetitions(dtype: Type[np.number], split: bool):
         for b0 in [0, 1]:
             for b1 in [0, 1]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0), cirq.measure(q1)
+                    (cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0), cirq.measure(q1)
                 )
                 result = simulator.run(circuit, repetitions=0)
                 np.testing.assert_equal(
@@ -312,7 +312,7 @@ def test_run_repetitions_measure_at_end(dtype: Type[np.number], split: bool):
         for b0 in [0, 1]:
             for b1 in [0, 1]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0), cirq.measure(q1)
+                    (cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0), cirq.measure(q1)
                 )
                 result = simulator.run(circuit, repetitions=3)
                 np.testing.assert_equal(result.measurements, {'0': [[b0]] * 3, '1': [[b1]] * 3})
@@ -329,7 +329,7 @@ def test_run_qudits_repetitions_measure_at_end(dtype: Type[np.number], split: bo
         for b0 in [0, 1]:
             for b1 in [0, 1, 2]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0), PlusGate(3, b1)(q1), cirq.measure(q0), cirq.measure(q1)
+                    (cirq.X**b0)(q0), PlusGate(3, b1)(q1), cirq.measure(q0), cirq.measure(q1)
                 )
                 result = simulator.run(circuit, repetitions=3)
                 np.testing.assert_equal(
@@ -348,8 +348,8 @@ def test_run_measurement_not_terminal_no_repetitions(dtype: Type[np.number], spl
         for b0 in [0, 1]:
             for b1 in [0, 1]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0),
-                    (cirq.X ** b1)(q1),
+                    (cirq.X**b0)(q0),
+                    (cirq.X**b1)(q1),
                     cirq.measure(q0),
                     cirq.measure(q1),
                     cirq.H(q0),
@@ -372,8 +372,8 @@ def test_run_repetitions_measurement_not_terminal(dtype: Type[np.number], split:
         for b0 in [0, 1]:
             for b1 in [0, 1]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0),
-                    (cirq.X ** b1)(q1),
+                    (cirq.X**b0)(q0),
+                    (cirq.X**b1)(q1),
                     cirq.measure(q0),
                     cirq.measure(q1),
                     cirq.H(q0),
@@ -394,7 +394,7 @@ def test_run_qudits_repetitions_measurement_not_terminal(dtype: Type[np.number],
         for b0 in [0, 1]:
             for b1 in [0, 1, 2]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0),
+                    (cirq.X**b0)(q0),
                     PlusGate(3, b1)(q1),
                     cirq.measure(q0),
                     cirq.measure(q1),
@@ -448,7 +448,7 @@ def test_run_measure_multiple_qubits(dtype: Type[np.number], split: bool):
     simulator = cirq.DensityMatrixSimulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0, q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0, q1))
             result = simulator.run(circuit, repetitions=3)
             np.testing.assert_equal(result.measurements, {'0,1': [[b0, b1]] * 3})
 
@@ -460,7 +460,7 @@ def test_run_measure_multiple_qudits(dtype: Type[np.number], split: bool):
     simulator = cirq.DensityMatrixSimulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1, 2]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), PlusGate(3, b1)(q1), cirq.measure(q0, q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), PlusGate(3, b1)(q1), cirq.measure(q0, q1))
             result = simulator.run(circuit, repetitions=3)
             np.testing.assert_equal(result.measurements, {'0 (d=2),1 (d=3)': [[b0, b1]] * 3})
 
@@ -628,7 +628,7 @@ def test_simulate_bit_flips(dtype: Type[np.number], split: bool):
     for b0 in [0, 1]:
         for b1 in [0, 1]:
             circuit = cirq.Circuit(
-                (cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0), cirq.measure(q1)
+                (cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0), cirq.measure(q1)
             )
             result = simulator.simulate(circuit)
             np.testing.assert_equal(result.measurements, {'0': [b0], '1': [b1]})
@@ -645,7 +645,7 @@ def test_simulate_qudit_increments(dtype: Type[np.number], split: bool):
     for b0 in [0, 1]:
         for b1 in [0, 1, 2]:
             circuit = cirq.Circuit(
-                (cirq.X ** b0)(q0), (PlusGate(3)(q1),) * b1, cirq.measure(q0), cirq.measure(q1)
+                (cirq.X**b0)(q0), (PlusGate(3)(q1),) * b1, cirq.measure(q0), cirq.measure(q1)
             )
             result = simulator.simulate(circuit)
             np.testing.assert_equal(result.measurements, {'0 (d=2)': [b0], '1 (d=3)': [b1]})
@@ -661,7 +661,7 @@ def test_simulate_initial_state(dtype: Type[np.number], split: bool):
     simulator = cirq.DensityMatrixSimulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1))
             result = simulator.simulate(circuit, initial_state=1)
             expected_density_matrix = np.zeros(shape=(4, 4))
             expected_density_matrix[b0 * 2 + 1 - b1, b0 * 2 + 1 - b1] = 1.0
@@ -675,7 +675,7 @@ def test_simulate_act_on_args(dtype: Type[np.number], split: bool):
     simulator = cirq.DensityMatrixSimulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1))
             args = simulator._create_act_on_args(initial_state=1, qubits=(q0, q1))
             result = simulator.simulate(circuit, initial_state=args)
             expected_density_matrix = np.zeros(shape=(4, 4))
@@ -688,7 +688,7 @@ def test_simulate_tps_initial_state():
     simulator = cirq.DensityMatrixSimulator()
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1))
             result = simulator.simulate(circuit, initial_state=cirq.KET_ZERO(q0) * cirq.KET_ONE(q1))
             expected_density_matrix = np.zeros(shape=(4, 4))
             expected_density_matrix[b0 * 2 + 1 - b1, b0 * 2 + 1 - b1] = 1.0
@@ -721,7 +721,7 @@ def test_simulate_qubit_order(dtype: Type[np.number], split: bool):
     simulator = cirq.DensityMatrixSimulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1))
             result = simulator.simulate(circuit, qubit_order=[q1, q0])
             expected_density_matrix = np.zeros(shape=(4, 4))
             expected_density_matrix[2 * b1 + b0, 2 * b1 + b0] = 1.0
@@ -754,7 +754,7 @@ def test_simulate_measure_multiple_qubits(dtype: Type[np.number], split: bool):
     simulator = cirq.DensityMatrixSimulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0, q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0, q1))
             result = simulator.simulate(circuit)
             np.testing.assert_equal(result.measurements, {'0,1': [b0, b1]})
 
@@ -766,7 +766,7 @@ def test_simulate_measure_multiple_qudits(dtype: Type[np.number], split: bool):
     simulator = cirq.DensityMatrixSimulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1, 2]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), PlusGate(3, b1)(q1), cirq.measure(q0, q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), PlusGate(3, b1)(q1), cirq.measure(q0, q1))
             result = simulator.simulate(circuit)
             np.testing.assert_equal(result.measurements, {'0 (d=2),1 (d=3)': [b0, b1]})
 
@@ -1112,30 +1112,24 @@ def test_density_matrix_trial_result_qid_shape():
     final_step_result._simulator_state.return_value = cirq.DensityMatrixSimulatorState(
         density_matrix=np.ones((4, 4)) / 4, qubit_map={q0: 0, q1: 1}
     )
-    assert (
-        cirq.qid_shape(
-            cirq.DensityMatrixTrialResult(
-                params=cirq.ParamResolver({}),
-                measurements={},
-                final_step_result=final_step_result,
-            ),
-        )
-        == (2, 2)
-    )
+    assert cirq.qid_shape(
+        cirq.DensityMatrixTrialResult(
+            params=cirq.ParamResolver({}),
+            measurements={},
+            final_step_result=final_step_result,
+        ),
+    ) == (2, 2)
     q0, q1 = cirq.LineQid.for_qid_shape((3, 4))
     final_step_result._simulator_state.return_value = cirq.DensityMatrixSimulatorState(
         density_matrix=np.ones((12, 12)) / 12, qubit_map={q0: 0, q1: 1}
     )
-    assert (
-        cirq.qid_shape(
-            cirq.DensityMatrixTrialResult(
-                params=cirq.ParamResolver({}),
-                measurements={},
-                final_step_result=final_step_result,
-            ),
-        )
-        == (3, 4)
-    )
+    assert cirq.qid_shape(
+        cirq.DensityMatrixTrialResult(
+            params=cirq.ParamResolver({}),
+            measurements={},
+            final_step_result=final_step_result,
+        ),
+    ) == (3, 4)
 
 
 def test_density_matrix_trial_result_repr():
diff --git a/cirq/sim/density_matrix_utils_test.py b/cirq/sim/density_matrix_utils_test.py
index da8d672a04a..80e72ef07ee 100644
--- a/cirq/sim/density_matrix_utils_test.py
+++ b/cirq/sim/density_matrix_utils_test.py
@@ -248,7 +248,7 @@ def test_measure_density_matrix_collapse():
 
 def test_measure_density_matrix_seed():
     n = 5
-    matrix = np.eye(2 ** n) / 2 ** n
+    matrix = np.eye(2**n) / 2**n
 
     bits, out_matrix1 = cirq.measure_density_matrix(matrix, range(n), seed=1234)
     assert bits == [False, False, True, True, False]
diff --git a/cirq/sim/mux_test.py b/cirq/sim/mux_test.py
index c76919a5686..2b47840cacb 100644
--- a/cirq/sim/mux_test.py
+++ b/cirq/sim/mux_test.py
@@ -197,10 +197,10 @@ def test_final_state_vector_param_resolver():
     s = sympy.Symbol('s')
 
     with pytest.raises(ValueError, match='not unitary'):
-        _ = cirq.final_state_vector(cirq.X ** s)
+        _ = cirq.final_state_vector(cirq.X**s)
 
     np.testing.assert_allclose(
-        cirq.final_state_vector(cirq.X ** s, param_resolver={s: 0.5}), [0.5 + 0.5j, 0.5 - 0.5j]
+        cirq.final_state_vector(cirq.X**s, param_resolver={s: 0.5}), [0.5 + 0.5j, 0.5 - 0.5j]
     )
 
 
@@ -312,10 +312,10 @@ def test_final_density_matrix_param_resolver():
     s = sympy.Symbol('s')
 
     with pytest.raises(ValueError, match='not specified in parameter sweep'):
-        _ = cirq.final_density_matrix(cirq.X ** s)
+        _ = cirq.final_density_matrix(cirq.X**s)
 
     np.testing.assert_allclose(
-        cirq.final_density_matrix(cirq.X ** s, param_resolver={s: 0.5}),
+        cirq.final_density_matrix(cirq.X**s, param_resolver={s: 0.5}),
         [[0.5 - 0.0j, 0.0 + 0.5j], [0.0 - 0.5j, 0.5 - 0.0j]],
     )
 
diff --git a/cirq/sim/sparse_simulator_test.py b/cirq/sim/sparse_simulator_test.py
index decc516ca42..4ebee4f32eb 100644
--- a/cirq/sim/sparse_simulator_test.py
+++ b/cirq/sim/sparse_simulator_test.py
@@ -85,7 +85,7 @@ def test_run_bit_flips(dtype: Type[np.number], split: bool):
     for b0 in [0, 1]:
         for b1 in [0, 1]:
             circuit = cirq.Circuit(
-                (cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0), cirq.measure(q1)
+                (cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0), cirq.measure(q1)
             )
             result = simulator.run(circuit)
             np.testing.assert_equal(result.measurements, {'0': [[b0]], '1': [[b1]]})
@@ -100,7 +100,7 @@ def test_run_measure_at_end_no_repetitions(dtype: Type[np.number], split: bool):
         for b0 in [0, 1]:
             for b1 in [0, 1]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0), cirq.measure(q1)
+                    (cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0), cirq.measure(q1)
                 )
                 result = simulator.run(circuit, repetitions=0)
                 np.testing.assert_equal(
@@ -126,7 +126,7 @@ def test_run_repetitions_measure_at_end(dtype: Type[np.number], split: bool):
         for b0 in [0, 1]:
             for b1 in [0, 1]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0), cirq.measure(q1)
+                    (cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0), cirq.measure(q1)
                 )
                 result = simulator.run(circuit, repetitions=3)
                 np.testing.assert_equal(result.measurements, {'0': [[b0]] * 3, '1': [[b1]] * 3})
@@ -144,8 +144,8 @@ def test_run_invert_mask_measure_not_terminal(dtype: Type[np.number], split: boo
         for b0 in [0, 1]:
             for b1 in [0, 1]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0),
-                    (cirq.X ** b1)(q1),
+                    (cirq.X**b0)(q0),
+                    (cirq.X**b1)(q1),
                     cirq.measure(q0, q1, key='m', invert_mask=(True, False)),
                     cirq.X(q0),
                 )
@@ -165,8 +165,8 @@ def test_run_partial_invert_mask_measure_not_terminal(dtype: Type[np.number], sp
         for b0 in [0, 1]:
             for b1 in [0, 1]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0),
-                    (cirq.X ** b1)(q1),
+                    (cirq.X**b0)(q0),
+                    (cirq.X**b1)(q1),
                     cirq.measure(q0, q1, key='m', invert_mask=(True,)),
                     cirq.X(q0),
                 )
@@ -186,8 +186,8 @@ def test_run_measurement_not_terminal_no_repetitions(dtype: Type[np.number], spl
         for b0 in [0, 1]:
             for b1 in [0, 1]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0),
-                    (cirq.X ** b1)(q1),
+                    (cirq.X**b0)(q0),
+                    (cirq.X**b1)(q1),
                     cirq.measure(q0),
                     cirq.measure(q1),
                     cirq.H(q0),
@@ -210,8 +210,8 @@ def test_run_repetitions_measurement_not_terminal(dtype: Type[np.number], split:
         for b0 in [0, 1]:
             for b1 in [0, 1]:
                 circuit = cirq.Circuit(
-                    (cirq.X ** b0)(q0),
-                    (cirq.X ** b1)(q1),
+                    (cirq.X**b0)(q0),
+                    (cirq.X**b1)(q1),
                     cirq.measure(q0),
                     cirq.measure(q1),
                     cirq.H(q0),
@@ -283,7 +283,7 @@ def test_run_measure_multiple_qubits(dtype: Type[np.number], split: bool):
     simulator = cirq.Simulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0, q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0, q1))
             result = simulator.run(circuit, repetitions=3)
             np.testing.assert_equal(result.measurements, {'0,1': [[b0, b1]] * 3})
 
@@ -443,7 +443,7 @@ def test_simulate_bit_flips(dtype: Type[np.number], split: bool):
     for b0 in [0, 1]:
         for b1 in [0, 1]:
             circuit = cirq.Circuit(
-                (cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0), cirq.measure(q1)
+                (cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0), cirq.measure(q1)
             )
             result = simulator.simulate(circuit)
             np.testing.assert_equal(result.measurements, {'0': [b0], '1': [b1]})
@@ -459,7 +459,7 @@ def test_simulate_initial_state(dtype: Type[np.number], split: bool):
     simulator = cirq.Simulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1))
             result = simulator.simulate(circuit, initial_state=1)
             expected_state = np.zeros(shape=(2, 2))
             expected_state[b0][1 - b1] = 1.0
@@ -473,7 +473,7 @@ def test_simulate_act_on_args(dtype: Type[np.number], split: bool):
     simulator = cirq.Simulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1))
             args = simulator._create_act_on_args(initial_state=1, qubits=(q0, q1))
             result = simulator.simulate(circuit, initial_state=args)
             expected_state = np.zeros(shape=(2, 2))
@@ -488,7 +488,7 @@ def test_simulate_qubit_order(dtype: Type[np.number], split: bool):
     simulator = cirq.Simulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1))
             result = simulator.simulate(circuit, qubit_order=[q1, q0])
             expected_state = np.zeros(shape=(2, 2))
             expected_state[b1][b0] = 1.0
@@ -521,7 +521,7 @@ def test_simulate_measure_multiple_qubits(dtype: Type[np.number], split: bool):
     simulator = cirq.Simulator(dtype=dtype, split_untangled_states=split)
     for b0 in [0, 1]:
         for b1 in [0, 1]:
-            circuit = cirq.Circuit((cirq.X ** b0)(q0), (cirq.X ** b1)(q1), cirq.measure(q0, q1))
+            circuit = cirq.Circuit((cirq.X**b0)(q0), (cirq.X**b1)(q1), cirq.measure(q0, q1))
             result = simulator.simulate(circuit)
             np.testing.assert_equal(result.measurements, {'0,1': [b0, b1]})
 
diff --git a/cirq/sim/state_vector_simulator_test.py b/cirq/sim/state_vector_simulator_test.py
index 69911517b8c..789224f975e 100644
--- a/cirq/sim/state_vector_simulator_test.py
+++ b/cirq/sim/state_vector_simulator_test.py
@@ -176,7 +176,7 @@ def test_str_big():
     args = cirq.ActOnStateVectorArgs(
         prng=np.random.RandomState(0),
         qubits=qs,
-        initial_state=np.array([1] * 2 ** 10, dtype=np.complex64) * 0.03125,
+        initial_state=np.array([1] * 2**10, dtype=np.complex64) * 0.03125,
         dtype=np.complex64,
     )
     final_step_result = cirq.SparseSimulatorStep(args, cirq.Simulator())
diff --git a/cirq/sim/state_vector_test.py b/cirq/sim/state_vector_test.py
index b0af39559cc..7c5928d1948 100644
--- a/cirq/sim/state_vector_test.py
+++ b/cirq/sim/state_vector_test.py
@@ -244,7 +244,7 @@ def test_measure_state_collapse():
 
 def test_measure_state_seed():
     n = 10
-    initial_state = np.ones(2 ** n) / 2 ** (n / 2)
+    initial_state = np.ones(2**n) / 2 ** (n / 2)
 
     bits, state1 = cirq.measure_state_vector(initial_state, range(n), seed=1234)
     np.testing.assert_equal(
diff --git a/cirq/testing/consistent_phase_by_test.py b/cirq/testing/consistent_phase_by_test.py
index 5bf4bf51bb8..03c9f46eff7 100644
--- a/cirq/testing/consistent_phase_by_test.py
+++ b/cirq/testing/consistent_phase_by_test.py
@@ -24,7 +24,7 @@ def __init__(self, e):
         self.e = e
 
     def _unitary_(self):
-        return np.array([[0, 1j ** -self.e], [1j ** self.e, 0]])
+        return np.array([[0, 1j**-self.e], [1j**self.e, 0]])
 
     def _phase_by_(self, phase_turns: float, qubit_index: int):
         return GoodPhaser(self.e + phase_turns * 4)
@@ -43,8 +43,8 @@ def _qid_shape_(self):
     def _unitary_(self):
         return np.array(
             [
-                [0, 1j ** -self.e, 0],
-                [0, 0, 1j ** self.e],
+                [0, 1j**-self.e, 0],
+                [0, 0, 1j**self.e],
                 [1, 0, 0],
             ]
         )
@@ -61,7 +61,7 @@ def __init__(self, e):
         self.e = e
 
     def _unitary_(self):
-        return np.array([[0, 1j ** -(self.e * 2)], [1j ** self.e, 0]])
+        return np.array([[0, 1j ** -(self.e * 2)], [1j**self.e, 0]])
 
     def _phase_by_(self, phase_turns: float, qubit_index: int):
         return BadPhaser(self.e + phase_turns * 4)
diff --git a/cirq/testing/consistent_protocols.py b/cirq/testing/consistent_protocols.py
index 8a759384b58..1c0e5666fbd 100644
--- a/cirq/testing/consistent_protocols.py
+++ b/cirq/testing/consistent_protocols.py
@@ -75,7 +75,7 @@ def assert_implements_consistent_protocols(
         p = protocols.pow(val, exponent, None)
         if p is not None:
             _assert_meets_standards_helper(
-                val ** exponent,
+                val**exponent,
                 ignoring_global_phase=ignoring_global_phase,
                 setup_code=setup_code,
                 global_vals=global_vals,
diff --git a/cirq/testing/consistent_protocols_test.py b/cirq/testing/consistent_protocols_test.py
index 8543f3ae16c..4c9ef31518c 100644
--- a/cirq/testing/consistent_protocols_test.py
+++ b/cirq/testing/consistent_protocols_test.py
@@ -41,8 +41,8 @@ def _has_unitary_(self):
     def _unitary_(self) -> Union[np.ndarray, NotImplementedType]:
         if cirq.is_parameterized(self):
             return NotImplemented
-        z = cirq.unitary(cirq.Z ** self.phase_exponent)
-        x = cirq.unitary(cirq.X ** self.exponent)
+        z = cirq.unitary(cirq.Z**self.phase_exponent)
+        x = cirq.unitary(cirq.X**self.exponent)
         return np.dot(np.dot(z, x), np.conj(z))
 
     def _apply_unitary_(self, args: cirq.ApplyUnitaryArgs) -> Union[np.ndarray, NotImplementedType]:
@@ -65,7 +65,7 @@ def _decompose_(self, qubits: Sequence[cirq.Qid]) -> cirq.OP_TREE:
         q = qubits[0]
         z = cirq.Z(q) ** self.phase_exponent
         x = cirq.X(q) ** self.exponent
-        return z ** -1, x, z
+        return z**-1, x, z
 
     def _pauli_expansion_(self) -> cirq.LinearDict[str]:
         if self._is_parameterized_():
@@ -159,7 +159,7 @@ def _decompose_(self, qubits: Sequence[cirq.Qid]) -> cirq.OP_TREE:
         if cirq.is_parameterized(z):
             # coverage: ignore
             return NotImplemented
-        return z ** -1, x, z
+        return z**-1, x, z
 
 
 class BadGatePauliExpansion(GoodGate):
diff --git a/cirq/testing/consistent_qasm.py b/cirq/testing/consistent_qasm.py
index a1672e7afff..bcad22f3333 100644
--- a/cirq/testing/consistent_qasm.py
+++ b/cirq/testing/consistent_qasm.py
@@ -139,5 +139,5 @@ def _reorder_indices_of_matrix(matrix: np.ndarray, new_order: List[int]):
     new_input_indices = new_order
     new_output_indices = [i + num_qubits for i in new_input_indices]
     matrix = np.moveaxis(matrix, all_indices, new_input_indices + new_output_indices)
-    matrix = np.reshape(matrix, (2 ** num_qubits, 2 ** num_qubits))
+    matrix = np.reshape(matrix, (2**num_qubits, 2**num_qubits))
     return matrix
diff --git a/cirq/testing/random_circuit_test.py b/cirq/testing/random_circuit_test.py
index 33bce27b536..9203ef0d0d8 100644
--- a/cirq/testing/random_circuit_test.py
+++ b/cirq/testing/random_circuit_test.py
@@ -92,7 +92,7 @@ def test_random_circuit(
     )
 
 
-@pytest.mark.parametrize('seed', [random.randint(0, 2 ** 32) for _ in range(10)])
+@pytest.mark.parametrize('seed', [random.randint(0, 2**32) for _ in range(10)])
 def test_random_circuit_reproducible_with_seed(seed):
     wrappers = (lambda s: s, np.random.RandomState)
     circuits = [
diff --git a/cirq/transformers/analytical_decompositions/clifford_decomposition.py b/cirq/transformers/analytical_decompositions/clifford_decomposition.py
index 6c782d59769..1e51d8b866e 100644
--- a/cirq/transformers/analytical_decompositions/clifford_decomposition.py
+++ b/cirq/transformers/analytical_decompositions/clifford_decomposition.py
@@ -51,7 +51,7 @@ def _Sdg(
     qubits: List['cirq.Qid'],
 ):
     # Apply the tableau with S^\{dagger}
-    protocols.act_on(ops.S ** -1, args, qubits=[qubits[q]], allow_decompose=False)
+    protocols.act_on(ops.S**-1, args, qubits=[qubits[q]], allow_decompose=False)
     operations.append(ops.S(qubits[q]))
 
 
diff --git a/cirq/transformers/analytical_decompositions/controlled_gate_decomposition.py b/cirq/transformers/analytical_decompositions/controlled_gate_decomposition.py
index b6d68f372a6..af01e926499 100644
--- a/cirq/transformers/analytical_decompositions/controlled_gate_decomposition.py
+++ b/cirq/transformers/analytical_decompositions/controlled_gate_decomposition.py
@@ -25,7 +25,7 @@
 
 
 def _unitary_power(matrix: np.ndarray, power: float) -> np.ndarray:
-    return map_eigenvalues(matrix, lambda e: e ** power)
+    return map_eigenvalues(matrix, lambda e: e**power)
 
 
 def _is_identity(matrix):
diff --git a/cirq/transformers/analytical_decompositions/single_qubit_decompositions_test.py b/cirq/transformers/analytical_decompositions/single_qubit_decompositions_test.py
index 5f15a6b87af..5b49bee62b0 100644
--- a/cirq/transformers/analytical_decompositions/single_qubit_decompositions_test.py
+++ b/cirq/transformers/analytical_decompositions/single_qubit_decompositions_test.py
@@ -86,13 +86,13 @@ def test_single_qubit_matrix_to_gates_known_z():
 def test_single_qubit_matrix_to_gates_known_s():
     actual = cirq.single_qubit_matrix_to_gates(np.array([[1, 0], [0, 1j]]), tolerance=0.01)
 
-    assert cirq.approx_eq(actual, [cirq.Z ** 0.5], atol=1e-9)
+    assert cirq.approx_eq(actual, [cirq.Z**0.5], atol=1e-9)
 
 
 def test_known_s_dag():
     actual = cirq.single_qubit_matrix_to_gates(np.array([[1, 0], [0, -1j]]), tolerance=0.01)
 
-    assert cirq.approx_eq(actual, [cirq.Z ** -0.5], atol=1e-9)
+    assert cirq.approx_eq(actual, [cirq.Z**-0.5], atol=1e-9)
 
 
 def test_known_h():
@@ -100,7 +100,7 @@ def test_known_h():
         np.array([[1, 1], [1, -1]]) * np.sqrt(0.5), tolerance=0.001
     )
 
-    assert cirq.approx_eq(actual, [cirq.Y ** -0.5, cirq.Z], atol=1e-9)
+    assert cirq.approx_eq(actual, [cirq.Y**-0.5, cirq.Z], atol=1e-9)
 
 
 @pytest.mark.parametrize(
@@ -189,10 +189,10 @@ def _random_unitary_with_close_eigenvalues():
         np.eye(2),
         cirq.unitary(cirq.H),
         cirq.unitary(cirq.X),
-        cirq.unitary(cirq.X ** 0.5),
+        cirq.unitary(cirq.X**0.5),
         cirq.unitary(cirq.Y),
         cirq.unitary(cirq.Z),
-        cirq.unitary(cirq.Z ** 0.5),
+        cirq.unitary(cirq.Z**0.5),
         _random_unitary_with_close_eigenvalues(),
     ]
     + [cirq.testing.random_unitary(2) for _ in range(10)],
@@ -214,16 +214,16 @@ def test_single_qubit_matrix_to_phased_x_z_known():
     assert cirq.approx_eq(actual, [cirq.Z], atol=1e-9)
 
     actual = cirq.single_qubit_matrix_to_phased_x_z(np.array([[1, 0], [0, 1j]]), atol=0.01)
-    assert cirq.approx_eq(actual, [cirq.Z ** 0.5], atol=1e-9)
+    assert cirq.approx_eq(actual, [cirq.Z**0.5], atol=1e-9)
 
     actual = cirq.single_qubit_matrix_to_phased_x_z(np.array([[1, 0], [0, -1j]]), atol=0.01)
-    assert cirq.approx_eq(actual, [cirq.Z ** -0.5], atol=1e-9)
+    assert cirq.approx_eq(actual, [cirq.Z**-0.5], atol=1e-9)
 
     actual = cirq.single_qubit_matrix_to_phased_x_z(
         np.array([[1, 1], [1, -1]]) * np.sqrt(0.5), atol=0.001
     )
     assert cirq.approx_eq(
-        actual, [cirq.PhasedXPowGate(phase_exponent=-0.5, exponent=0.5), cirq.Z ** -1], atol=1e-9
+        actual, [cirq.PhasedXPowGate(phase_exponent=-0.5, exponent=0.5), cirq.Z**-1], atol=1e-9
     )
 
 
diff --git a/cirq/transformers/analytical_decompositions/two_qubit_to_cz.py b/cirq/transformers/analytical_decompositions/two_qubit_to_cz.py
index ac3d9dae0d3..9d455ed789d 100644
--- a/cirq/transformers/analytical_decompositions/two_qubit_to_cz.py
+++ b/cirq/transformers/analytical_decompositions/two_qubit_to_cz.py
@@ -251,8 +251,8 @@ def _non_local_part(
 
     if allow_partial_czs or all(_is_trivial_angle(e, atol) for e in [x, y, z]):
         return [
-            _parity_interaction(q0, q1, x, atol, ops.Y ** -0.5),
-            _parity_interaction(q0, q1, y, atol, ops.X ** 0.5),
+            _parity_interaction(q0, q1, x, atol, ops.Y**-0.5),
+            _parity_interaction(q0, q1, y, atol, ops.X**0.5),
             _parity_interaction(q0, q1, z, atol),
         ]
 
diff --git a/cirq/transformers/analytical_decompositions/two_qubit_to_cz_test.py b/cirq/transformers/analytical_decompositions/two_qubit_to_cz_test.py
index ebd22a23d2d..08e6374c088 100644
--- a/cirq/transformers/analytical_decompositions/two_qubit_to_cz_test.py
+++ b/cirq/transformers/analytical_decompositions/two_qubit_to_cz_test.py
@@ -137,8 +137,8 @@ def assert_ops_implement_unitary(q0, q1, operations, intended_effect, atol=0.01)
                 ]
             ),
         ),
-        (0, 0, cirq.unitary(cirq.CZ ** 0.00000001)),
-        (0.5, 2, cirq.unitary(cirq.CZ ** 0.5)),
+        (0, 0, cirq.unitary(cirq.CZ**0.00000001)),
+        (0.5, 2, cirq.unitary(cirq.CZ**0.5)),
         (1, 1, cirq.unitary(cirq.CZ)),
         (1, 1, cirq.unitary(cirq.CNOT)),
         (
@@ -180,7 +180,7 @@ def assert_ops_implement_unitary(q0, q1, operations, intended_effect, atol=0.01)
             )
             * np.sqrt(0.5),
         ),
-        (1.5, 3, cirq.map_eigenvalues(cirq.unitary(cirq.SWAP), lambda e: e ** 0.5)),
+        (1.5, 3, cirq.map_eigenvalues(cirq.unitary(cirq.SWAP), lambda e: e**0.5)),
         (2, 2, cirq.unitary(cirq.SWAP).dot(cirq.unitary(cirq.CZ))),
         (3, 3, cirq.unitary(cirq.SWAP)),
         (
@@ -250,7 +250,7 @@ def test_kak_decomposition_depth_full_cz():
     assert len(c) > 6  # Length should be 13 with extra Pauli gates
 
     # Partial single-axis interaction.
-    u = cirq.unitary(cirq.CNOT ** 0.1)
+    u = cirq.unitary(cirq.CNOT**0.1)
     operations_with_part = cirq.two_qubit_matrix_to_cz_operations(a, b, u, False)
     c = cirq.Circuit(operations_with_part)
     # 2 CZ, 2+1 PhasedX, 1 Z
@@ -282,7 +282,7 @@ def test_kak_decomposition_depth_partial_cz():
     assert len(c) <= 6
 
     # Partial single-axis interaction.
-    u = cirq.unitary(cirq.CNOT ** 0.1)
+    u = cirq.unitary(cirq.CNOT**0.1)
     operations_with_part = cirq.two_qubit_matrix_to_cz_operations(a, b, u, True)
     c = cirq.Circuit(operations_with_part)
     # 1 CP, 1+1 PhasedX, 1 Z
diff --git a/cirq/transformers/analytical_decompositions/two_qubit_to_fsim_test.py b/cirq/transformers/analytical_decompositions/two_qubit_to_fsim_test.py
index 2f4aadbbd7e..73106b28db8 100644
--- a/cirq/transformers/analytical_decompositions/two_qubit_to_fsim_test.py
+++ b/cirq/transformers/analytical_decompositions/two_qubit_to_fsim_test.py
@@ -40,7 +40,7 @@ def test_deprecated_submodule():
 
 UNITARY_OBJS = [
     cirq.IdentityGate(2),
-    cirq.XX ** 0.25,
+    cirq.XX**0.25,
     cirq.CNOT,
     cirq.CNOT(*cirq.LineQubit.range(2)),
     cirq.CNOT(*cirq.LineQubit.range(2)[::-1]),
diff --git a/cirq/transformers/analytical_decompositions/two_qubit_to_sqrt_iswap.py b/cirq/transformers/analytical_decompositions/two_qubit_to_sqrt_iswap.py
index 0fabfc32fcb..4cdb8898dc5 100644
--- a/cirq/transformers/analytical_decompositions/two_qubit_to_sqrt_iswap.py
+++ b/cirq/transformers/analytical_decompositions/two_qubit_to_sqrt_iswap.py
@@ -370,13 +370,13 @@ def append(matrix0, matrix1, final_layer=False):
             # Commute rightmost Z(q0)**b, Z(q1)**b through next sqrt-iSWAP
             if len(rots1) > 0 and rots1[-1][0] == ops.Z:
                 _, prev_z = rots1.pop()
-                z_unitary = protocols.unitary(ops.Z ** prev_z)
+                z_unitary = protocols.unitary(ops.Z**prev_z)
                 new_commute = new_commute @ z_unitary
                 matrix0 = z_unitary.T.conj() @ matrix0
             # Commute rightmost whole X(q0), X(q0) or Y, Y through next sqrt-iSWAP
             if len(rots1) > 0 and linalg.tolerance.near_zero_mod(rots1[-1][1], 1, atol=atol):
                 pauli, half_turns = rots1.pop()
-                p_unitary = protocols.unitary(pauli ** half_turns)
+                p_unitary = protocols.unitary(pauli**half_turns)
                 new_commute = new_commute @ p_unitary
                 matrix0 = p_unitary.T.conj() @ matrix0
         rots0 = list(
@@ -385,8 +385,8 @@ def append(matrix0, matrix1, final_layer=False):
             )
         )
         # Append single qubit ops
-        operations.extend((pauli ** half_turns).on(q0) for pauli, half_turns in rots0)
-        operations.extend((pauli ** half_turns).on(q1) for pauli, half_turns in rots1)
+        operations.extend((pauli**half_turns).on(q0) for pauli, half_turns in rots0)
+        operations.extend((pauli**half_turns).on(q1) for pauli, half_turns in rots1)
         prev_commute = new_commute
 
     single_ops = list(single_qubit_operations)
diff --git a/cirq/transformers/analytical_decompositions/two_qubit_to_sqrt_iswap_test.py b/cirq/transformers/analytical_decompositions/two_qubit_to_sqrt_iswap_test.py
index 5d37f64d678..d0542b17f59 100644
--- a/cirq/transformers/analytical_decompositions/two_qubit_to_sqrt_iswap_test.py
+++ b/cirq/transformers/analytical_decompositions/two_qubit_to_sqrt_iswap_test.py
@@ -127,12 +127,12 @@ def perturbations_weyl(x, y, z, amount=1e-10):
 ]
 TWO_SQRT_ISWAP_UNITARIES = [
     # Typical gates and nearby Weyl coordinates to simulate numerical noise
-    *perturbations_gate(cirq.XX ** 0.25),
-    *perturbations_gate(cirq.YY ** 0.07),
-    *perturbations_gate(cirq.ZZ ** 0.15),
+    *perturbations_gate(cirq.XX**0.25),
+    *perturbations_gate(cirq.YY**0.07),
+    *perturbations_gate(cirq.ZZ**0.15),
     *perturbations_gate(cirq.CNOT),
     *perturbations_gate(cirq.ISWAP),
-    *perturbations_gate(cirq.ISWAP ** 0.1),
+    *perturbations_gate(cirq.ISWAP**0.1),
     # Critical points in the Weyl chamber and nearby coordinates to simulate numerical noise
     *perturbations_weyl(np.pi / 4, 0, 0),
     *perturbations_weyl(np.pi / 4, np.pi / 4, 0),
@@ -389,7 +389,7 @@ def test_decomp3(u):
 
 def test_decomp3_invalid():
     # All two-qubit gates can be synthesized with three SQRT_ISWAP gates
-    u = cirq.unitary(cirq.X ** 0.2)  # Pass an invalid size unitary
+    u = cirq.unitary(cirq.X**0.2)  # Pass an invalid size unitary
     q0, q1 = cirq.LineQubit.range(2)
     with pytest.raises(ValueError, match='Input must correspond to a 4x4 unitary matrix'):
         cirq.two_qubit_matrix_to_sqrt_iswap_operations(q0, q1, u, required_sqrt_iswap_count=3)
diff --git a/cirq/transformers/eject_phased_paulis_test.py b/cirq/transformers/eject_phased_paulis_test.py
index b0e545250dc..9ef93c97777 100644
--- a/cirq/transformers/eject_phased_paulis_test.py
+++ b/cirq/transformers/eject_phased_paulis_test.py
@@ -65,7 +65,7 @@ def assert_optimizes(
     # Nested sub-circuits should also get optimized.
     q = before.all_qubits()
     c_nested = cirq.Circuit(
-        [cirq.PhasedXPowGate(phase_exponent=0.5).on_each(*q), (cirq.Z ** 0.5).on_each(*q)],
+        [cirq.PhasedXPowGate(phase_exponent=0.5).on_each(*q), (cirq.Z**0.5).on_each(*q)],
         cirq.CircuitOperation(before.freeze()).repeat(2).with_tags("ignore"),
         [cirq.Y.on_each(*q), cirq.X.on_each(*q)],
         cirq.CircuitOperation(before.freeze()).repeat(3).with_tags("preserve_tag"),
diff --git a/cirq/transformers/eject_z_test.py b/cirq/transformers/eject_z_test.py
index d5bf72931fb..7c0daae894a 100644
--- a/cirq/transformers/eject_z_test.py
+++ b/cirq/transformers/eject_z_test.py
@@ -45,17 +45,17 @@ def assert_optimizes(
     # Nested sub-circuits should also get optimized.
     q = before.all_qubits()
     c_nested = cirq.Circuit(
-        [(cirq.Z ** 0.5).on_each(*q), (cirq.Y ** 0.25).on_each(*q)],
+        [(cirq.Z**0.5).on_each(*q), (cirq.Y**0.25).on_each(*q)],
         cirq.Moment(cirq.CircuitOperation(before.freeze()).repeat(2).with_tags("ignore")),
-        [(cirq.Z ** 0.5).on_each(*q), (cirq.Y ** 0.25).on_each(*q)],
+        [(cirq.Z**0.5).on_each(*q), (cirq.Y**0.25).on_each(*q)],
         cirq.Moment(cirq.CircuitOperation(before.freeze()).repeat(3).with_tags("preserve_tag")),
     )
     c_expected = cirq.Circuit(
         cirq.PhasedXPowGate(phase_exponent=0, exponent=0.25).on_each(*q),
-        (cirq.Z ** 0.5).on_each(*q),
+        (cirq.Z**0.5).on_each(*q),
         cirq.Moment(cirq.CircuitOperation(before.freeze()).repeat(2).with_tags("ignore")),
         cirq.PhasedXPowGate(phase_exponent=0, exponent=0.25).on_each(*q),
-        (cirq.Z ** 0.5).on_each(*q),
+        (cirq.Z**0.5).on_each(*q),
         cirq.Moment(cirq.CircuitOperation(expected.freeze()).repeat(3).with_tags("preserve_tag")),
     )
     if context is None:
diff --git a/cirq/transformers/measurement_transformers_test.py b/cirq/transformers/measurement_transformers_test.py
index cb46c0ff357..9280cd4bf39 100644
--- a/cirq/transformers/measurement_transformers_test.py
+++ b/cirq/transformers/measurement_transformers_test.py
@@ -24,7 +24,7 @@ def assert_equivalent_to_deferred(circuit: cirq.Circuit):
     qubits = list(circuit.all_qubits())
     sim = cirq.Simulator()
     num_qubits = len(qubits)
-    for i in range(2 ** num_qubits):
+    for i in range(2**num_qubits):
         bits = cirq.big_endian_int_to_bits(i, bit_count=num_qubits)
         modified = cirq.Circuit()
         for j in range(num_qubits):
diff --git a/cirq/transformers/merge_k_qubit_gates_test.py b/cirq/transformers/merge_k_qubit_gates_test.py
index 6dc1434dc52..1135ce3a1d4 100644
--- a/cirq/transformers/merge_k_qubit_gates_test.py
+++ b/cirq/transformers/merge_k_qubit_gates_test.py
@@ -44,7 +44,7 @@ def test_merge_1q_unitaries():
     assert len(op_list) == 1
     assert isinstance(op_list[0].gate, cirq.MatrixGate)
     cirq.testing.assert_allclose_up_to_global_phase(
-        cirq.unitary(c), cirq.unitary(cirq.Y ** 0.5), atol=1e-7
+        cirq.unitary(c), cirq.unitary(cirq.Y**0.5), atol=1e-7
     )
 
     # 2. Gets blocked at a 2q operation.
diff --git a/cirq/transformers/target_gatesets/cz_gateset_test.py b/cirq/transformers/target_gatesets/cz_gateset_test.py
index fba184f05dc..14b89cab966 100644
--- a/cirq/transformers/target_gatesets/cz_gateset_test.py
+++ b/cirq/transformers/target_gatesets/cz_gateset_test.py
@@ -174,7 +174,7 @@ def test_optimizes_single_iswap():
 
 def test_optimizes_tagged_partial_cz():
     a, b = cirq.LineQubit.range(2)
-    c = cirq.Circuit((cirq.CZ ** 0.5)(a, b).with_tags('mytag'))
+    c = cirq.Circuit((cirq.CZ**0.5)(a, b).with_tags('mytag'))
     assert_optimization_not_broken(c)
     c = cirq.optimize_for_target_gateset(c, gateset=cirq.CZTargetGateset())
     assert (
diff --git a/cirq/value/digits_test.py b/cirq/value/digits_test.py
index afc8077afa4..a9f5ec1f937 100644
--- a/cirq/value/digits_test.py
+++ b/cirq/value/digits_test.py
@@ -70,7 +70,7 @@ def test_big_endian_int_to_digits():
     with pytest.raises(ValueError, match='Out of range'):
         assert cirq.big_endian_int_to_digits(101, base=[], digit_count=0) == []
     with pytest.raises(ValueError, match='Out of range'):
-        _ = cirq.big_endian_int_to_digits(10 ** 100, base=[2, 3, 4, 5, 6])
+        _ = cirq.big_endian_int_to_digits(10**100, base=[2, 3, 4, 5, 6])
 
     assert cirq.big_endian_int_to_digits(0, base=[], digit_count=0) == []
     assert cirq.big_endian_int_to_digits(0, base=[]) == []
diff --git a/cirq/value/duration_test.py b/cirq/value/duration_test.py
index 8ca572e0bd8..3ee689adf92 100644
--- a/cirq/value/duration_test.py
+++ b/cirq/value/duration_test.py
@@ -47,14 +47,14 @@ def test_init():
 
 def test_init_timedelta():
     assert Duration(timedelta(microseconds=0)).total_picos() == 0
-    assert Duration(timedelta(microseconds=513)).total_picos() == 513 * 10 ** 6
-    assert Duration(timedelta(microseconds=-5)).total_picos() == -5 * 10 ** 6
-    assert Duration(timedelta(microseconds=211)).total_picos() == 211 * 10 ** 6
-
-    assert Duration(timedelta(seconds=3)).total_picos() == 3 * 10 ** 12
-    assert Duration(timedelta(seconds=-5)).total_picos() == -5 * 10 ** 12
-    assert Duration(timedelta(seconds=3)).total_nanos() == 3 * 10 ** 9
-    assert Duration(timedelta(seconds=-5)).total_nanos() == -5 * 10 ** 9
+    assert Duration(timedelta(microseconds=513)).total_picos() == 513 * 10**6
+    assert Duration(timedelta(microseconds=-5)).total_picos() == -5 * 10**6
+    assert Duration(timedelta(microseconds=211)).total_picos() == 211 * 10**6
+
+    assert Duration(timedelta(seconds=3)).total_picos() == 3 * 10**12
+    assert Duration(timedelta(seconds=-5)).total_picos() == -5 * 10**12
+    assert Duration(timedelta(seconds=3)).total_nanos() == 3 * 10**9
+    assert Duration(timedelta(seconds=-5)).total_nanos() == -5 * 10**9
 
 
 def test_total():
diff --git a/cirq/value/linear_dict_test.py b/cirq/value/linear_dict_test.py
index cc59fc6e66d..0d1ff5575e3 100644
--- a/cirq/value/linear_dict_test.py
+++ b/cirq/value/linear_dict_test.py
@@ -499,10 +499,10 @@ def test_incomparable(a, b):
         ({}, '{}', '0'),
         ({}, '{:.2f}', '0.00'),
         ({}, '{:.2e}', '0.00e+00'),
-        ({'X': 2 ** -10}, '{:.2f}', '0.00'),
+        ({'X': 2**-10}, '{:.2f}', '0.00'),
         ({'X': 1 / 100}, '{:.2e}', '1.00e-02*X'),
-        ({'X': 1j * 2 ** -10}, '{:.2f}', '0.00'),
-        ({'X': 1j * 2 ** -10}, '{:.3f}', '0.001j*X'),
+        ({'X': 1j * 2**-10}, '{:.2f}', '0.00'),
+        ({'X': 1j * 2**-10}, '{:.3f}', '0.001j*X'),
         ({'X': 2j, 'Y': -3}, '{:.2f}', '2.00j*X-3.00*Y'),
         ({'X': -2j, 'Y': 3}, '{:.2f}', '-2.00j*X+3.00*Y'),
         ({'X': np.sqrt(1j)}, '{:.3f}', '(0.707+0.707j)*X'),
diff --git a/cirq/value/random_state_test.py b/cirq/value/random_state_test.py
index 14990f5dd6a..694965ea0a9 100644
--- a/cirq/value/random_state_test.py
+++ b/cirq/value/random_state_test.py
@@ -33,7 +33,7 @@ def rand(prng):
     eq = cirq.testing.EqualsTester()
     eq.add_equality_group(*vals)
 
-    seed = np.random.randint(2 ** 31)
+    seed = np.random.randint(2**31)
     prngs = [
         np.random.RandomState(seed),
         cirq.value.parse_random_state(np.random.RandomState(seed)),
diff --git a/cirq/value/timestamp.py b/cirq/value/timestamp.py
index 7833a8c9716..f5c35dfc41a 100644
--- a/cirq/value/timestamp.py
+++ b/cirq/value/timestamp.py
@@ -49,7 +49,7 @@ def raw_picos(self) -> float:
 
     def __add__(self, other) -> 'Timestamp':
         if isinstance(other, timedelta):
-            return Timestamp(picos=self._picos + other.total_seconds() * 10 ** 12)
+            return Timestamp(picos=self._picos + other.total_seconds() * 10**12)
         if not isinstance(other, Duration):
             return NotImplemented
         return Timestamp(picos=self._picos + other.total_picos())
@@ -70,7 +70,7 @@ def __sub__(self, other):
         if isinstance(other, Duration):
             return Timestamp(picos=self._picos - other.total_picos())
         if isinstance(other, timedelta):
-            return Timestamp(picos=self._picos - other.total_seconds() * 10 ** 12)
+            return Timestamp(picos=self._picos - other.total_seconds() * 10**12)
         if isinstance(other, type(self)):
             return Duration(picos=self._picos - other._picos)
         return NotImplemented
diff --git a/cirq/vis/density_matrix.py b/cirq/vis/density_matrix.py
index 4cf726f77f4..3a06644cd31 100644
--- a/cirq/vis/density_matrix.py
+++ b/cirq/vis/density_matrix.py
@@ -105,12 +105,12 @@ def plot_density_matrix(
 
     matrix = matrix.astype(np.complex128)
     num_qubits = int(np.log2(matrix.shape[0]))
-    validate_density_matrix(matrix, qid_shape=(2 ** num_qubits,))
+    validate_density_matrix(matrix, qid_shape=(2**num_qubits,))
 
     if ax is None:
         _, ax = plt.subplots(figsize=(10, 10))
-    ax.set_xlim(0 - _padding_around_plot, 2 ** num_qubits + _padding_around_plot)
-    ax.set_ylim(0 - _padding_around_plot, 2 ** num_qubits + _padding_around_plot)
+    ax.set_xlim(0 - _padding_around_plot, 2**num_qubits + _padding_around_plot)
+    ax.set_ylim(0 - _padding_around_plot, 2**num_qubits + _padding_around_plot)
 
     for i in range(matrix.shape[0]):
         for j in range(matrix.shape[1]):
diff --git a/cirq/vis/state_histogram.py b/cirq/vis/state_histogram.py
index 7bb15cc6aab..d8dcdeb9bb0 100644
--- a/cirq/vis/state_histogram.py
+++ b/cirq/vis/state_histogram.py
@@ -32,7 +32,7 @@ def get_state_histogram(result: 'result.Result') -> np.ndarray:
         The state histogram (a numpy array) corresponding to the trial result.
     """
     num_qubits = sum([value.shape[1] for value in result.measurements.values()])
-    states = 2 ** num_qubits
+    states = 2**num_qubits
     values = np.zeros(states)
     # measurements is a dict of {measurement gate key:
     #                            array(repetitions, boolean result)}
diff --git a/cirq/work/observable_measurement_data.py b/cirq/work/observable_measurement_data.py
index b4da1a87faf..b638e9f426f 100644
--- a/cirq/work/observable_measurement_data.py
+++ b/cirq/work/observable_measurement_data.py
@@ -485,7 +485,7 @@ def variance(self, setting: InitObsSetting, *, atol: float = 1e-8):
 
             # https://en.wikipedia.org/wiki/Propagation_of_uncertainty#Example_formulae
             # assume cov(a,b) = 0, otherwise there would be another term.
-            var = f ** 2 * (var_a / (a ** 2) + var_b / (b ** 2))
+            var = f**2 * (var_a / (a**2) + var_b / (b**2))
 
         return var
 
diff --git a/cirq/work/observable_measurement_data_test.py b/cirq/work/observable_measurement_data_test.py
index 9382a646d17..3054640bfc6 100644
--- a/cirq/work/observable_measurement_data_test.py
+++ b/cirq/work/observable_measurement_data_test.py
@@ -77,7 +77,7 @@ def test_stats_from_measurements():
     # 10 [each obs val deviates by 10]. The variance is 10**2 and the
     # squared-standard-error-of-the-mean can be found by dividing by the
     # number of samples minus 1.
-    assert err == 10 ** 2 / (4 - 1)
+    assert err == 10**2 / (4 - 1)
 
 
 def test_observable_measured_result():
@@ -89,7 +89,7 @@ def test_observable_measured_result():
             observable=cirq.Y(a) * cirq.Y(b),
         ),
         mean=0,
-        variance=5 ** 2,
+        variance=5**2,
         repetitions=4,
         circuit_params={'phi': 52},
     )
@@ -381,16 +381,16 @@ def test_bitstring_accumulator_stats():
     # so the total contribution is zero, and the matrix is diagonal
     should_be = np.array(
         [
-            [4 * 7 ** 2, 0, 0],
-            [0, 4 * 5 ** 2, 0],
-            [0, 0, 4 * 3 ** 2],
+            [4 * 7**2, 0, 0],
+            [0, 4 * 5**2, 0],
+            [0, 0, 4 * 3**2],
         ]
     )
     should_be = should_be / (4 - 1)  # covariance formula
     should_be = should_be / 4  # cov of the distribution of sample mean
     np.testing.assert_allclose(should_be, bsa.covariance())
 
-    for setting, var in zip(settings, [4 * 7 ** 2, 4 * 5 ** 2, 4 * 3 ** 2]):
+    for setting, var in zip(settings, [4 * 7**2, 4 * 5**2, 4 * 3**2]):
         np.testing.assert_allclose(0, bsa.mean(setting))
         np.testing.assert_allclose(var / 4 / (4 - 1), bsa.variance(setting))
         np.testing.assert_allclose(np.sqrt(var / 4 / (4 - 1)), bsa.stderr(setting))
@@ -447,7 +447,7 @@ def test_bitstring_accumulator_stats_2():
     should_be = should_be / 4  # cov of the distribution of sample mean
     np.testing.assert_allclose(should_be, bsa.covariance())
 
-    for setting, var in zip(settings, [4 * 5 ** 2, 4 * 3 ** 2]):
+    for setting, var in zip(settings, [4 * 5**2, 4 * 3**2]):
         np.testing.assert_allclose(0, bsa.mean(setting))
         np.testing.assert_allclose(var / 4 / (4 - 1), bsa.variance(setting))
         np.testing.assert_allclose(np.sqrt(var / 4 / (4 - 1)), bsa.stderr(setting))
diff --git a/cirq/work/observable_measurement_test.py b/cirq/work/observable_measurement_test.py
index 4a51b138b74..02a801db5c3 100644
--- a/cirq/work/observable_measurement_test.py
+++ b/cirq/work/observable_measurement_test.py
@@ -549,7 +549,7 @@ def test_XYZ_point8(circuit, observable):
         circuit,
         [observable],
         cirq.Simulator(seed=52),
-        stopping_criteria=VarianceStoppingCriteria(1e-3 ** 2),
+        stopping_criteria=VarianceStoppingCriteria(1e-3**2),
     )
     assert len(df) == 1, 'one observable'
     mean = df.loc[0]['mean']