input: 
  from typing import List
  
  
  def optimize_equation(equation: str) -> str:
      """ Optimizes an equation by combining like terms and representing them in a simplified form.
      >>> optimize_equation('x + x + y + y + y')
      'x^2 + y^3'
      >>> optimize_equation('a + b + b + a + a + c + c + c + c')
      'a^3 + b^2 + c^4'
      """
  
      terms = equation.split('+')
      variables = {}
  
      for term in terms:
          var = term.strip()
          if var in variables:
              variables[var] += 1
          else:
              variables[var] = 1
  
      new_equation = []
      for var, count in variables.items():
          new_equation.append(f'{var}^{count}')
  
      return ' + '.join(new_equation)
  
output:     terms = equation.split('+')
      variables = {}
  
      for term in terms:
          var = term.strip()
          if var in variables:
              variables[var] += 1
          else:
              variables[var] = 1
  
      new_equation = []
      for var, count in variables.items():
          new_equation.append(f'{var}^{count}')
  
      return ' + '.join(new_equation)