code: def test_FreeGroupElm_ext_rep():
      assert (x**2 * z**-2 * x).ext_rep == (
          Symbol("x"),
          2,
          Symbol("z"),
          -2,
          Symbol("x"),
          1,
      )
      assert (x**-2 * y**-1).ext_rep == (
          Symbol("x"),
          -2,
          Symbol("y"),
          -1,
      )
      assert (x * z).ext_rep == (Symbol("x"), 1, Symbol("z"), 1)
  
imports: from sympy.combinatorics.free_groups import free_group, FreeGroup
  from sympy.core import Symbol
  from sympy.testing.pytest import raises
  from sympy.core.numbers import oo
label_desc: Use image node_id 14 for calling a global function with example usage: test_FreeGroupElm_ext_rep() without return types