What is the units digit of 7^282

Hello,

Let's assume the last digit given by the function last (x).

last (7^0) = 1

last (7) = 7

last (7^2) = last (49) = 9

last (7^3) = last (last (7^2) * 7) = last (9*7) = last (63) = 3

last (7^4) = 1

If the exponent n is 0,4,8,12, ... a multiple of 4 last (7^n) = 1

If the exponent n is 1,5,9,13, ... a multiple of 4 + 1 last (7^n) = 7

If the exponent n is 2,6,10,14, ... a multiple of 4 + 2 last (7^n) = 9

If the exponent n is 3,7,11,15, ... a multiple of 4 + 3 last (7^n) = 37

Here exponent is 282=70*4+2

last (7^282) = 9