Question

14^(27) = ? mod 55

Answer 1

cant get that

Answer 2

14 = 14 mod 55
14^2 = 196 = 31 mod 55
...

Answer 3

14^4 = (14^2)^2 = 31^2 =961 = 26 mod 55

Answer 4

27 = 1+2+8+16

Answer 5

14^8= (14^4)^2 = 26^2 =676=16 mod 55

Answer 6

14^(16) = (14^8)^2 = 16^2 = 256 = 36 mod 55

Answer 7

14^27 = 14^1 * 14^2 * 14^8 *14^16
=14*31*16*36=249984=9 mod 55

Answer 8

14^3 = 49 mod 55
49^3 = 4 mod 55
4^3 = 9 mod 55

14^27 = 9 mod 55
Not really sure if you can do this!!!
http://www.wolframalpha.com/input/?i=mod%2814^%2827%29%2C55%29

Answer 9

experiment x, seems OK.
The repeated squares is reliable in all cases, no guessing...