How can I prove that:
$ (g^b \bmod{p})^a \bmod{p} = (g^a \bmod{p})^b \bmod{p}$
where p is a prime number, g is a primitive root of p, and a and b are integers.
While I understand that $(g^b)^a = (g^a)^b$ , I cannot figure out how to deal with the mod functions...