diff --git a/pandas/core/base.py b/pandas/core/base.py
index 40ff0640a5bc4..0685ce5c92815 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -4,7 +4,7 @@
 
 import builtins
 import textwrap
-from typing import Dict, FrozenSet, List, Optional, Union
+from typing import Any, Dict, FrozenSet, List, Optional, Union
 
 import numpy as np
 
@@ -49,6 +49,8 @@ class PandasObject(DirNamesMixin):
     Baseclass for various pandas objects.
     """
 
+    _cache: Dict[str, Any]
+
     @property
     def _constructor(self):
         """
@@ -63,7 +65,7 @@ def __repr__(self) -> str:
         # Should be overwritten by base classes
         return object.__repr__(self)
 
-    def _reset_cache(self, key=None):
+    def _reset_cache(self, key: Optional[str] = None) -> None:
         """
         Reset cached properties. If ``key`` is passed, only clears that key.
         """
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 31966489403f4..d73c5de0253e8 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -1,7 +1,7 @@
 from datetime import datetime
 import operator
 from textwrap import dedent
-from typing import TYPE_CHECKING, Any, Dict, FrozenSet, Hashable, Union
+from typing import TYPE_CHECKING, Any, FrozenSet, Hashable, Union
 import warnings
 
 import numpy as np
@@ -250,7 +250,6 @@ def _outer_indexer(self, left, right):
 
     _typ = "index"
     _data: Union[ExtensionArray, np.ndarray]
-    _cache: Dict[str, Any]
     _id = None
     _name: Label = None
     # MultiIndex.levels previously allowed setting the index name. We