input: def optimize_equation(equation: str) -> str:
      """Given an equation as a string of terms separated by '+', optimize it 
      by combining like terms and representing them in the form 'variable^count'.
      >>> optimize_equation('x + x + y + y + y')
      'x^2 + y^3'
      >>> optimize_equation('a + b + a + a + a + c + c + c + c')
      'a^4 + b + c^4'
      """
      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:     from collections import defaultdict
  
      term_counts = defaultdict(int)
      for term in equation.split('+'):
          var = term.strip()
          term_counts[var] += 1
  
      optimized_terms = []
      for var, count in term_counts.items():
          if count > 1:
              optimized_terms.append(f"{var}^{count}")
          else:
              optimized_terms.append(var)
  
      return ' + '.join(optimized_terms)