Find the last two digits of the number 11^2016 .

I need to figure out how to hand do this and show all my work. Help pls

1 answer

Start a table of the powers of 11
n 11^n
1 11
2 121
3 1331
4 14641

The last 2 digits just cycle through
11
21
31
...
91
01
11
21
...
So, 11^2016 ends in 61

Or, you might find this article on modular arithmetic useful:

https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/fast-modular-exponentiation