- What is the last digit of 2^2015 ?

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If you check the powers of 2 such as 2,4,8,16,32,64,128,256,…, you can find the pattern of the last digit 2,4,8,6,2,4,8,6,… which has a repeated sequence of period of 4 . Now you can divide the power by 4 and if it gives remainder as 1 last digit is 2 , if the remainder is 2 last digit is 4 , if the remainder is 3 last digit is 8 and if the remainder is 0 last digit is 6.

In your case the power 2015 divided by 4 gives remainder 3 . Therefore last digit should be 8. Hope this way may be helpful to solve your problem.