diff --git a/cirq-core/cirq/ops/pauli_gates.py b/cirq-core/cirq/ops/pauli_gates.py
index 85f3b881bca..4465697d2dc 100644
--- a/cirq-core/cirq/ops/pauli_gates.py
+++ b/cirq-core/cirq/ops/pauli_gates.py
@@ -108,7 +108,7 @@ def __init__(self):
         common_gates.XPowGate.__init__(self, exponent=1.0)
 
     def __pow__(self: '_PauliX', exponent: 'cirq.TParamVal') -> common_gates.XPowGate:
-        return common_gates.XPowGate(exponent=exponent)
+        return common_gates.XPowGate(exponent=exponent) if exponent != 1 else _PauliX()
 
     def _with_exponent(self: '_PauliX', exponent: 'cirq.TParamVal') -> common_gates.XPowGate:
         return self.__pow__(exponent)
@@ -135,7 +135,7 @@ def __init__(self):
         common_gates.YPowGate.__init__(self, exponent=1.0)
 
     def __pow__(self: '_PauliY', exponent: 'cirq.TParamVal') -> common_gates.YPowGate:
-        return common_gates.YPowGate(exponent=exponent)
+        return common_gates.YPowGate(exponent=exponent) if exponent != 1 else _PauliY()
 
     def _with_exponent(self: '_PauliY', exponent: 'cirq.TParamVal') -> common_gates.YPowGate:
         return self.__pow__(exponent)
@@ -162,7 +162,7 @@ def __init__(self):
         common_gates.ZPowGate.__init__(self, exponent=1.0)
 
     def __pow__(self: '_PauliZ', exponent: 'cirq.TParamVal') -> common_gates.ZPowGate:
-        return common_gates.ZPowGate(exponent=exponent)
+        return common_gates.ZPowGate(exponent=exponent) if exponent != 1 else _PauliZ()
 
     def _with_exponent(self: '_PauliZ', exponent: 'cirq.TParamVal') -> common_gates.ZPowGate:
         return self.__pow__(exponent)
diff --git a/cirq-core/cirq/ops/pauli_gates_test.py b/cirq-core/cirq/ops/pauli_gates_test.py
index b4e375f41e0..81753b5f019 100644
--- a/cirq-core/cirq/ops/pauli_gates_test.py
+++ b/cirq-core/cirq/ops/pauli_gates_test.py
@@ -216,3 +216,7 @@ def test_powers():
     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)