Series.pow when right operand is missing value
diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index b29d35c8ce332..4f5f31da75e03 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -317,6 +317,7 @@ Timezones
 Numeric
 ^^^^^^^
 - Bug in :func:`read_csv` with ``engine="pyarrow"`` causing rounding errors for large integers (:issue:`52505`)
+- Bug in :meth:`Series.pow` not filling missing values correctly (:issue:`55512`)
 -
 
 Conversion
diff --git a/pandas/core/series.py b/pandas/core/series.py
index c6e1e460b336a..724a54c85da9b 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -6043,6 +6043,8 @@ def _flex_method(self, other, op, *, level=None, fill_value=None, axis: Axis = 0
             return result
         else:
             if fill_value is not None:
+                if isna(other):
+                    return op(self, fill_value)
                 self = self.fillna(fill_value)
 
             return op(self, other)
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 86aef2642750e..f9fcfd19e9956 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -3017,6 +3017,14 @@ def test_arrowextensiondtype_dataframe_repr():
     assert result == expected
 
 
+def test_pow_missing_operand():
+    # GH 55512
+    k = pd.Series([2, None], dtype="int64[pyarrow]")
+    result = k.pow(None, fill_value=3)
+    expected = pd.Series([8, None], dtype="int64[pyarrow]")
+    tm.assert_series_equal(result, expected)
+
+
 @pytest.mark.parametrize("pa_type", tm.TIMEDELTA_PYARROW_DTYPES)
 def test_duration_fillna_numpy(pa_type):
     # GH 54707

- [x] closes #55512 (Replace xxxx with the GitHub issue number)
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [x] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.
