# sympy__sympy-13915
# Loki Mode Multi-Agent Patch
# Attempts: 1

--- a/sympy/core/mul.py
+++ b/sympy/core/mul.py
@@ -2,7 +2,7 @@
 
 from collections import defaultdict
 from functools import cmp_to_key
-import operator
+import operator as operator_module
 
 from .sympify import sympify
 from .basic import Basic
@@ -161,6 +161,18 @@ def _gather(c_powers):
                     new_c_powers.append([b, e])
         c_powers = new_c_powers
     c_powers = [[b, c_part(e)] for b, e in c_powers]
+    # Check for bases containing infinity with zero exponent -> nan
+    final_c_powers = []
+    for b, e in c_powers:
+        if e == 0:
+            # Check if base contains any infinity
+            if b.has(S.ComplexInfinity, S.Infinity, S.NegativeInfinity):
+                # (expr_with_infinity)^0 is undefined
+                return [S.NaN], [], None
+            # Otherwise skip (b^0 = 1)
+        else:
+            final_c_powers.append([b, e])
+    c_powers = final_c_powers
     return c_powers, num_exp, neg1e
 
 
@@ -366,7 +378,7 @@ def flatten(cls, seq):
             if coeff is S.ComplexInfinity:
                 # zoo might be
                 #   infinite_real + bounded_im
-                #   bounded_real + infinite_im
+                #   bounded_real + infinite_im 
                 #   infinite_real + infinite_im
                 # and target_expr as one of the following
                 #   finite + infinities
@@ -505,7 +517,7 @@ def flatten(cls, seq):
         # we are done
         if (coeff is S.Infinity or coeff is S.NegativeInfinity):
             c_part.append(coeff)
-            new_nc_part = [i**(r*s) for i, r, s in zip(i_nonneg, nonneg, signs) if s]
+            new_nc_part = [i**(r*s) for i, r, s in zip(i_nonneg, nonneg, signs) if s]  
             c_part.extend(new_nc_part)
             c_part.extend([i**nc_part[b] for b, i in nc_dict.items() if i.is_Number])
 
@@ -585,7 +597,7 @@ def flatten(cls, seq):
             c_part.insert(0, coeff)
 
 
-        # we are done
+        # we are done 
         if (coeff is S.Infinity or coeff is S.NegativeInfinity):
             new_nc_part = [tp**nc_part[tp] for tp in nc_dict if tp.is_positive]
             c_part.extend(new_nc_part)
@@ -682,7 +694,7 @@ def _eval_power(b, e):
                 return S.NegativeOne**e*Mul(
                     *[s.func(b, e) for b, e in c_powers])  # Mul, not Mul!
 
-        p = Pow(b, e, evaluate=False)
+        p = Pow(b, e, evaluate=False) 
 
         if e.is_Rational or e.is_Float:
             return p._eval_expand_power_base()