Question

what is the remainder when 32^32^32 is divided by 7?

Answer 1

Use modulo 7, reduce it to 4^4^4. Then expand step by step reducing along the way. So (16)^2^4, gives 9^2^4 gives 81^4 gives 4^4 gives (16)^2 gives 81 which has remainder 4.

Answer 2

Or obviously do it faster since 9 is 2 mod 7.