input: from typing import List, Tuple
  
  def optimize_equation(equation: str) -> str:
      """
      Optimizes a given equation by reducing like terms and representing the equation in a simplified form.
      The input equation is a string where each term is separated by ' + '; each term is of the format 'variable count'.
      The output is the optimized equation where like terms are combined using the '^' symbol.
  
      >>> optimize_equation('x + x + y + y + y')
      'x^2 + y^3'
      >>> optimize_equation('a + a + a + b + b')
      'a^3 + b^2'
      """
      variables = {}
      for term in equation.split('+'):
          var, count = term.strip().split(' ')
          variables[var] = variables.get(var, 0) + int(count)
  
      new_equation = ""
      for var, count in variables.items():
          new_equation += var + '^' + str(count) + ' + '
      return new_equation[:-3]
output:     variables = {}
      for term in equation.split('+'):
          var, count = term.strip().split(' ')
          variables[var] = variables.get(var, 0) + int(count)
  
      new_equation = ""
      for var, count in variables.items():
          new_equation += var + '^' + str(count) + ' + '
      return new_equation[:-3]