# sympy__sympy-18087
# Loki Mode Multi-Agent Patch
# Attempts: 1

Based on the architect's analysis, this is a SymPy repository issue. Since the SymPy codebase is not present in the current working directory, I'll generate the patch based on the provided analysis of the bug in the `Factors` class.

```
--- a/sympy/core/exprtools.py
+++ b/sympy/core/exprtools.py
@@ -449,10 +449,16 @@ class Factors(dict):
                         b, e = b.as_base_exp()
                         if e is not S.One:
                             e = Mul(e, p)
-                            p = S.One
-                        b, e = Pow(b, e).as_base_exp()  # in case it is unevaluated
+                            # Only collapse exponents when mathematically valid:
+                            # (b^e)^p = b^(e*p) is valid when e is integer,
+                            # or b is positive, or p is integer
+                            if e.is_integer or b.is_positive or p.is_integer:
+                                p = S.One
+                                b, e = Pow(b, e).as_base_exp()
+                            else:
+                                # Keep as (b^e)^p form
+                                b = Pow(b, e/p)
+                                e = p
                     else:
                         b, e = b.as_base_exp()
-
                 if b is S.One:
```

Wait, let me reconsider. The patch needs to be more precise based on the actual code structure. Let me provide a cleaner patch:

--- a/sympy/core/exprtools.py
+++ b/sympy/core/exprtools.py
@@ -449,9 +449,17 @@ class Factors(dict):
                     if p is not S.One:
                         b, e = b.as_base_exp()
                         if e is not S.One:
-                            e = Mul(e, p)
-                            p = S.One
-                        b, e = Pow(b, e).as_base_exp()  # in case it is unevaluated
+                            # Only collapse (b^e)^p to b^(e*p) when mathematically valid:
+                            # This requires e to be an integer, b to be positive, or p to be an integer
+                            if e.is_integer or b.is_positive or p.is_integer:
+                                e = Mul(e, p)
+                                p = S.One
+                                b, e = Pow(b, e).as_base_exp()  # in case it is unevaluated
+                            else:
+                                # Keep the original form - don't simplify sqrt(x**2) to x
+                                b = Pow(b, e)
+                                e = p
+                                p = S.One
                     else:
                         b, e = b.as_base_exp()