Find the remainder when 84^79 is divided by 100

Ans = 64 We've to find 84^79 mod 100 = (100-16)^79 mod 100 = -1* 16^79 mod 100 (as by binomial expansion this is the last and only term not divisible by 100, before this term each term has some power of 100) = -1* (2^4)^79 mod 100 = - 1 * 2^316 mod 100 = -1 * (2^6) * (2^10)^31 mod 100 = -64 * (1024)^31 mod 100 (We need to focus on last 2 digits, 24^even mod 100 = 76 24^odd mod 100 = 24) = -64 * 24 mod 100 = 36 * 24 mod 100 = 864 mod 100 = 64