diff --git a/cirq/ops/raw_types.py b/cirq/ops/raw_types.py
index e5600fec6c6..17af8bf991f 100644
--- a/cirq/ops/raw_types.py
+++ b/cirq/ops/raw_types.py
@@ -825,8 +825,8 @@ def _trace_distance_bound_(self) -> float:
     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
+    def __pow__(self, exponent: Any) -> 'cirq.TaggedOperation':
+        return TaggedOperation(self.sub_operation ** exponent, *self.tags)
 
     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 d2be7c029e1..866bcf4f26e 100644
--- a/cirq/ops/raw_types_test.py
+++ b/cirq/ops/raw_types_test.py
@@ -422,6 +422,7 @@ def test_tagged_operation():
     op = cirq.X(q1).with_tags('tag1')
     op_repr = "cirq.X(cirq.GridQubit(1, 1))"
     assert repr(op) == f"cirq.TaggedOperation({op_repr}, 'tag1')"
+    assert op == op ** 1
 
     assert op.qubits == (q1,)
     assert op.tags == ('tag1',)
@@ -616,7 +617,7 @@ 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).with_tags(tag)
     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)