code: def refine_Pow(expr, assumptions):
      """
      Handler for instances of Pow.
  
      Examples
      ========
  
      >>> from sympy import Q
      >>> from sympy.assumptions.refine import refine_Pow
      >>> from sympy.abc import x,y,z
      >>> refine_Pow((-1)**x, Q.real(x))
      >>> refine_Pow((-1)**x, Q.even(x))
      1
      >>> refine_Pow((-1)**x, Q.odd(x))
      -1
  
      For powers of -1, even parts of the exponent can be simplified:
  
      >>> refine_Pow((-1)**(x+y), Q.even(x))
      (-1)**y
      >>> refine_Pow((-1)**(x+y+z), Q.odd(x) & Q.odd(z))
      (-1)**y
      >>> refine_Pow((-1)**(x+y+2), Q.odd(x))
      (-1)**(y + 1)
      >>> refine_Pow((-1)**(x+3), True)
      (-1)**(x + 1)
  
      """
      from sympy.functions.elementary.complexes import Abs
      from sympy.functions import sign
  
      if isinstance(expr.base, Abs):
          if ask(Q.real(expr.base.args[0]), assumptions) and ask(
              Q.even(expr.exp), assumptions
          ):
              return expr.base.args[0] ** expr.exp
      if ask(Q.real(expr.base), assumptions):
          if expr.base.is_number:
              if ask(Q.even(expr.exp), assumptions):
                  return abs(expr.base) ** expr.exp
              if ask(Q.odd(expr.exp), assumptions):
                  return sign(expr.base) * abs(expr.base) ** expr.exp
          if isinstance(expr.exp, Rational):
              if isinstance(expr.base, Pow):
                  return abs(expr.base.base) ** (
                      expr.base.exp * expr.exp
                  )
  
          if expr.base is S.NegativeOne:
              if expr.exp.is_Add:
                  old = expr
  
                  # For powers of (-1) we can remove
                  #  - even terms
                  #  - pairs of odd terms
                  #  - a single odd term + 1
                  #  - A numerical constant N can be replaced with mod(N,2)
  
                  coeff, terms = expr.exp.as_coeff_add()
                  terms = set(terms)
                  even_terms = set()
                  odd_terms = set()
                  initial_number_of_terms = len(terms)
  
                  for t in terms:
                      if ask(Q.even(t), assumptions):
                          even_terms.add(t)
                      elif ask(Q.odd(t), assumptions):
                          odd_terms.add(t)
  
                  terms -= even_terms
                  if len(odd_terms) % 2:
                      terms -= odd_terms
                      new_coeff = (coeff + S.One) % 2
                  else:
                      terms -= odd_terms
                      new_coeff = coeff % 2
  
                  if (
                      new_coeff != coeff
                      or len(terms) < initial_number_of_terms
                  ):
                      terms.add(new_coeff)
                      expr = expr.base ** (Add(*terms))
  
                  # Handle (-1)**((-1)**n/2 + m/2)
                  e2 = 2 * expr.exp
                  if ask(Q.even(e2), assumptions):
                      if e2.could_extract_minus_sign():
                          e2 *= expr.base
                  if e2.is_Add:
                      i, p = e2.as_two_terms()
                      if p.is_Pow and p.base is S.NegativeOne:
                          if ask(Q.integer(p.exp), assumptions):
                              i = (i + 1) / 2
                              if ask(Q.even(i), assumptions):
                                  return expr.base**p.exp
                              elif ask(Q.odd(i), assumptions):
                                  return expr.base ** (p.exp + 1)
                              else:
                                  return expr.base ** (p.exp + i)
  
                  if old != expr:
                      return expr
  
file_path: sympy/sympy/assumptions/refine.py
imports: from __future__ import annotations
  from typing import Callable
  from sympy.core import S, Add, Expr, Basic, Mul, Pow, Rational
  from sympy.core.logic import fuzzy_not
  from sympy.logic.boolalg import Boolean
  from sympy.assumptions import ask, Q
label_desc: Use image node_id 3 for calling a global function with example usage: refine_Pow(expr, assumptions) and returns: unknown, unknown, unknown, unknown, expr, unknown, unknown, unknown