Q:

Does GMPY2 (or GMP) have a pow() function?

GMPY2 (or GMP) has a powmod function but I can't find anything for regular exponentiation aside from python's native pow. Does a function like this exist for mpz integers?

A:

Just use Python's standard pow() function or the exponentiation ** operator. GMPY2's mpz type overloads all the standard special methods so you should just be able to use standard Python commands.
For example:
>>> from gmpy2 import mpz
>>> pow(mpz(3),7)
mpz(2187)
>>> pow(mpz(3),7,13)
mpz(3)
>>> mpz(3)**7
mpz(2187)
>>> 

The same holds true for divmod(), etc.

