code: def test_expand_radicals():
      a = (x + y) ** R(1, 2)
  
      assert (a**1).expand() == a
      assert (a**3).expand() == x * a + y * a
      assert (
          a**5
      ).expand() == x**2 * a + 2 * x * y * a + y**2 * a
  
      assert (1 / a**1).expand() == 1 / a
      assert (1 / a**3).expand() == 1 / (x * a + y * a)
      assert (1 / a**5).expand() == 1 / (
          x**2 * a + 2 * x * y * a + y**2 * a
      )
  
      a = (x + y) ** R(1, 3)
  
      assert (a**1).expand() == a
      assert (a**2).expand() == a**2
      assert (a**4).expand() == x * a + y * a
      assert (a**5).expand() == x * a**2 + y * a**2
      assert (
          a**7
      ).expand() == x**2 * a + 2 * x * y * a + y**2 * a
  
imports: from sympy.core.expr import unchanged
  from sympy.core.mul import Mul
  from sympy.core.numbers import I, Rational, pi
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol
  from sympy.functions.combinatorial.factorials import factorial
  from sympy.functions.elementary.exponential import exp, log
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import cos, sin
  from sympy.series.order import O
  from sympy.simplify.radsimp import expand_numer
  from sympy.core.function import expand, expand_multinomial, expand_power_base, expand_log
  from sympy.testing.pytest import raises
  from sympy.core.random import verify_numerically
  from sympy.abc import x, y, z
label_desc: Use image node_id 5 for calling a global function with example usage: test_expand_radicals() without return types