Find the remainder when `27^(40)` is divided by 12.

Explanation

We have , ` 27^(40) = (3^(3))^(40) = 3^(120) = 3*(3)^(119) = 3*(4-1)^(119)`
` = 3(4n-1)`, where n is some integer
` = 12n- 3 = 12n- 12 + 9 = 12 (n-1) + 9`
= 12 + 9 , where m is some integer .
`therefore (27^(40))/(12) = m + (9)/(12)`
Hence , the remainder is 9 .