diff --git a/Doc/whatsnew/3.10.rst b/Doc/whatsnew/3.10.rst
index c4a79b6a1e98fa..5ea65fcf0126e7 100644
--- a/Doc/whatsnew/3.10.rst
+++ b/Doc/whatsnew/3.10.rst
@@ -285,6 +285,10 @@ Other Language Changes
   ``__globals__['__builtins__']``.
   (Contributed by Mark Shannon in :issue:`42990`.)
 
+* `**=` will try ``__pow__``/``__rpow__`` when ``__ipow__`` returns
+  :class:`NotImplemented` as defined by the language specification.
+  (Contributed by Brett Cannon in :issue:`38302`.)
+
 
 New Modules
 ===========
diff --git a/Lib/test/test_descr.py b/Lib/test/test_descr.py
index f0048f42f882b0..bbeaeb0b2824ed 100644
--- a/Lib/test/test_descr.py
+++ b/Lib/test/test_descr.py
@@ -3903,6 +3903,25 @@ def __ipow__(self, other):
         a = C()
         a **= 2
 
+    def test_pow_fallback_for_ipow(self):
+        # If __ipow__ returns NotImplemented, call __pow__.
+        # https://bugs.python.org/issue38302
+        class C:
+            def __init__(self, val):
+                self._val = val
+
+            def __ipow__(self, other):
+                return NotImplemented
+
+            def __pow__(self, other):
+                return self._val ** other
+
+        base = 3
+        exponent = 5
+        a = C(base)
+        a **= exponent
+        self.assertEqual(a, base ** exponent)
+
     def test_mutable_bases(self):
         # Testing mutable bases...
 
diff --git a/Misc/NEWS.d/next/Core and Builtins/2021-02-19-15-17-50.bpo-38302.Je4zmv.rst b/Misc/NEWS.d/next/Core and Builtins/2021-02-19-15-17-50.bpo-38302.Je4zmv.rst
new file mode 100644
index 00000000000000..e2ed938ffbb081
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2021-02-19-15-17-50.bpo-38302.Je4zmv.rst	
@@ -0,0 +1 @@
+When __ipow__ returns NotImplemented, fall back to trying __pow__/__rpow__.
diff --git a/Objects/abstract.c b/Objects/abstract.c
index c93309b352774c..e5f08616338562 100644
--- a/Objects/abstract.c
+++ b/Objects/abstract.c
@@ -845,6 +845,31 @@ binop_type_error(PyObject *v, PyObject *w, const char *op_name)
     return NULL;
 }
 
+static PyObject *
+ternaryop_type_error(PyObject *v, PyObject *w, PyObject *z, const char *op_name)
+{
+    if (z == Py_None) {
+        PyErr_Format(
+            PyExc_TypeError,
+            "unsupported operand type(s) for %.100s: "
+            "'%.100s' and '%.100s'",
+            op_name,
+            Py_TYPE(v)->tp_name,
+            Py_TYPE(w)->tp_name);
+    }
+    else {
+        PyErr_Format(
+            PyExc_TypeError,
+            "unsupported operand type(s) for %.100s: "
+            "'%.100s', '%.100s', '%.100s'",
+            op_name,
+            Py_TYPE(v)->tp_name,
+            Py_TYPE(w)->tp_name,
+            Py_TYPE(z)->tp_name);
+    }
+    return NULL;
+}
+
 static PyObject *
 binary_op(PyObject *v, PyObject *w, const int op_slot, const char *op_name)
 {
@@ -952,24 +977,7 @@ ternary_op(PyObject *v,
         }
     }
 
-    if (z == Py_None) {
-        PyErr_Format(
-            PyExc_TypeError,
-            "unsupported operand type(s) for ** or pow(): "
-            "'%.100s' and '%.100s'",
-            Py_TYPE(v)->tp_name,
-            Py_TYPE(w)->tp_name);
-    }
-    else {
-        PyErr_Format(
-            PyExc_TypeError,
-            "unsupported operand type(s) for pow(): "
-            "'%.100s', '%.100s', '%.100s'",
-            Py_TYPE(v)->tp_name,
-            Py_TYPE(w)->tp_name,
-            Py_TYPE(z)->tp_name);
-    }
-    return NULL;
+    Py_RETURN_NOTIMPLEMENTED;
 }
 
 #ifdef NDEBUG
@@ -1077,7 +1085,12 @@ PyNumber_Remainder(PyObject *v, PyObject *w)
 PyObject *
 PyNumber_Power(PyObject *v, PyObject *w, PyObject *z)
 {
-    return TERNARY_OP(v, w, z, NB_SLOT(nb_power), "** or pow()");
+    PyObject *result = TERNARY_OP(v, w, z, NB_SLOT(nb_power), "** or pow()");
+    if (result == Py_NotImplemented) {
+        Py_DECREF(result);
+        return ternaryop_type_error(v, w, z, "** or pow()");
+    }
+    return result;
 }
 
 /* Binary in-place operators */
@@ -1237,13 +1250,16 @@ PyNumber_InPlaceRemainder(PyObject *v, PyObject *w)
 PyObject *
 PyNumber_InPlacePower(PyObject *v, PyObject *w, PyObject *z)
 {
-    if (Py_TYPE(v)->tp_as_number &&
-        Py_TYPE(v)->tp_as_number->nb_inplace_power != NULL) {
-        return TERNARY_OP(v, w, z, NB_SLOT(nb_inplace_power), "**=");
-    }
-    else {
-        return TERNARY_OP(v, w, z, NB_SLOT(nb_power), "**=");
+    PyObject *result = TERNARY_OP(v, w, z, NB_SLOT(nb_inplace_power), "**=");
+    if (result == Py_NotImplemented) {
+        Py_DECREF(result);
+        result = TERNARY_OP(v, w, z, NB_SLOT(nb_power), "**=");
+        if (result == Py_NotImplemented) {
+            Py_DECREF(result);
+            return ternaryop_type_error(v, w, z, "**=");
+        }
     }
+    return result;
 }