diff --git a/ChangeLog b/ChangeLog
index 47e74120e0..23bd762d02 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -12,6 +12,9 @@ What's New in astroid 2.12.1?
 =============================
 Release date: TBA
 
+* Fix a crash when ``None`` (or a value inferred as ``None``) participates in a
+  ``**`` expression.
+
 * Fix a crash involving properties within ``if`` blocks.
 
 
diff --git a/astroid/protocols.py b/astroid/protocols.py
index 6a6523513d..a7f35ea4a6 100644
--- a/astroid/protocols.py
+++ b/astroid/protocols.py
@@ -121,6 +121,8 @@ def const_infer_binary_op(self, opnode, operator, other, context, _):
         if (
             operator == "**"
             and isinstance(self, nodes.Const)
+            and isinstance(self.value, (int, float))
+            and isinstance(other.value, (int, float))
             and (self.value > 1e5 or other.value > 1e5)
         ):
             yield not_implemented
diff --git a/tests/unittest_protocols.py b/tests/unittest_protocols.py
index dfac90193e..63765a5ea5 100644
--- a/tests/unittest_protocols.py
+++ b/tests/unittest_protocols.py
@@ -275,6 +275,10 @@ def test_uninferable_exponents() -> None:
         parsed = extract_node("15 ** 20220609")
         assert parsed.inferred() == [Uninferable]
 
+        # Test a pathological case (more realistic: None as naive inference result)
+        parsed = extract_node("None ** 2")
+        assert parsed.inferred() == [Uninferable]
+
 
 @pytest.mark.skipif(not PY38_PLUS, reason="needs assignment expressions")
 def test_named_expr_inference() -> None: