def explicit_exponentiation(a, b):
    output = 1
    top = b
    if (b < 0):
        top *= -1
    for i in range(top):
        output *= a
    if b < 0:
        return 1/output
    else:
        return output



def recursive_exponentiation(a, b):
   if b == 0:
       return 1
   else:
       if b < 0:
           return (1/a)*recursive_exponentiation(a, b+1)
       else:
           return a * recursive_exponentiation(a, b-1)