input: 
  def optimize_equation(equation):
      """
      This function takes an equation as input and returns an optimized version of the equation. 
      The equation is represented as a string of terms separated by ' + '. 
      Each term is expected to have a variable and its count, separated by a space. 
      The function combines the same variables and returns an optimized equation with each variable raised to the power of its combined count.
      
      Example:
      >>> optimize_equation('x + x + y + y + y')
      'x^2 + y^3'
      """
      variables = []
      for term in equation.split('+'):
          var, count = term.strip().split(' ')
          variables.append((var, int(count)))
  
      new_equation = ""
      for var, count in variables:
          new_equation += (var + '^' + str(count)) + ' + '
      return new_equation[:-3]
  
output:     variables_dict = {}
      for var, count in variables:
          if var in variables_dict:
              variables_dict[var] += count
          else:
              variables_dict[var] = count
  
      optimized_terms = []
      for var, count in variables_dict.items():
          if count > 1:
              optimized_terms.append(f"{var}^{count}")
          else:
              optimized_terms.append(var)
  
      return ' + '.join(optimized_terms)