Question

what is the last digit of 7²⁰¹⁵?

Answer 1

Answer :

We know

7¹ = 7

7² = 49 , Last digit is 9

7³ = 343 , Last digit is 3

7⁴ = 2401 , Last digit is 1

And

7⁵ = 16807 , Last digit is 7

So, we can see that after power 4 last digits repeat itself . And

$\frac{2015}{4}=503+\frac{3}{4}$ , So

^{$7^{4\times 503}=7^{2012}=lastdigitis1$}
Then
7²⁰¹⁵ have last digit = 3 ( Ans )