1. The problem statement, all variables and given/known data 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). 2. Relevant equations 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. 3. 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.