I am required to prove/disprove the theorem:
If a_1 is congruent to b_1 (mod n) and a_2 is congruent to b_2 (mod n), then (a_1)^(a_2) is congruent to (b_1)^(b_2) (mod n).
a_1 is congruent to b_1(mod n) can also be expressed as b_1=a_1+q*n where q is an integer.
The Attempt at a Solution
"There exist q, q' which are elements of Z such that (b_1)^(b_2) = (a_1+q*n)^(a_2+q'*n).
We can express (a_1+q*n)^(a_2+q'*n) as (a_1+q*n)^(a_2) + (a_1+q*n)^(q'*n)."
I don't think I am heading in the right direction. Is mathematical induction needed to prove this theorem?
Thanks in advance to anyone who can provide some insight.