code: def test_issue_3449():
      # test if powers are simplified correctly
      # see also issue 3995
      assert ((x ** Rational(1, 3)) ** Rational(2)) == x ** Rational(
          2, 3
      )
      assert ((x ** Rational(3)) ** Rational(2, 5)) == (
          x ** Rational(3)
      ) ** Rational(2, 5)
  
      a = Symbol("a", real=True)
      b = Symbol("b", real=True)
      assert (a**2) ** b == (abs(a) ** b) ** 2
      assert sqrt(1 / a) != 1 / sqrt(a)  # e.g. for a = -1
      assert (a**3) ** Rational(1, 3) != a
      assert (x**a) ** b != x ** (a * b)  # e.g. x = -1, a=2, b=1/2
      assert (x**0.5) ** b == x ** (0.5 * b)
      assert (x**0.5) ** 0.5 == x**0.25
      assert (x**2.5) ** 0.5 != x**1.25  # e.g. for x = 5*I
  
      k = Symbol("k", integer=True)
      m = Symbol("m", integer=True)
      assert (x**k) ** m == x ** (k * m)
      assert Number(5) ** Rational(2, 3) == Number(25) ** Rational(1, 3)
  
      assert (x**0.5) ** 2 == x**1.0
      assert (x**2) ** k == (x**k) ** 2 == x ** (2 * k)
  
      a = Symbol("a", positive=True)
      assert (a**3) ** Rational(2, 5) == a ** Rational(6, 5)
      assert (a**2) ** b == (a**b) ** 2
      assert (
          (a ** Rational(2, 3)) ** x
          == a ** (x * Rational(2, 3))
          != (a**x) ** Rational(2, 3)
      )
  
imports: from sympy.core import Basic, Rational, Symbol, S, Float, Integer, Mul, Number, Pow, Expr, I, nan, pi, symbols, oo, zoo, N
  from sympy.core.parameters import global_parameters
  from sympy.core.tests.test_evalf import NS
  from sympy.core.function import expand_multinomial
  from sympy.functions.elementary.miscellaneous import sqrt, cbrt
  from sympy.functions.elementary.exponential import exp, log
  from sympy.functions.special.error_functions import erf
  from sympy.functions.elementary.trigonometric import sin, cos, tan, sec, csc, atan
  from sympy.functions.elementary.hyperbolic import cosh, sinh, tanh
  from sympy.polys import Poly
  from sympy.series.order import O
  from sympy.sets import FiniteSet
  from sympy.core.power import power
  from sympy.core.intfunc import integer_nthroot
  from sympy.testing.pytest import warns, _both_exp_pow
  from sympy.utilities.exceptions import SymPyDeprecationWarning
  from sympy.abc import a, b, c, x, y
label_desc: Use image node_id 5 for calling a global function with example usage: test_issue_3449() without return types