Finished

                 # There is expression, which couldn't change by
                 # as_numer_denom(). E.g. n**(2/3) + 1 --> (n**(2/3) + 1, 1).
                 # We have to catch this case.
+                p = sum([self._eval_product(i, (k, a, n)) for i in p.as_coeff_Add()])
+                # For Add terms, we cannot safely evaluate the product in general
+                # as the current logic using as_coeff_Add() is incorrect.
+                # Return None to let the product remain unevaluated rather than
+                # producing wrong results.
+                return None
             else:
                 p = self._eval_product(p, (k, a, n))
+                if p is None:
+                    return None
             return p / q
         elif term.is_Mul:

Boom