I’m trying to algebraic calculations where both the variable and the exponent are symbols. But it seems that sympy does not fully understand the meaning of law of exponents:

>>> from sympy import *
>>> u, n = symbols('u n')
>>> u**(2*n) / u**n         # this is good
u**n
>>> u**n / u                # not good
u**n/u
>>> u**n * u                # not good
u*u**n

What can I do to get sympy to turn

u**n / u

into

u**(n-1)

and

u**n * u

into

u**(n+1)?

Thanks!