Last Digit of Powers

Last digits cycle every few powers — pin the exponent to the cycle.

Last digit of 7^43 = 3

Multiply by 7 and the last digit walks a ring: 7, 9, 3, 1, then 7 again.

The ring closes after 4 steps, so only 43 mod 4 = 3 decides where you land.

Ten whole laps land back at the start, and three more steps reach 3.

Your turn

Three to try in your head — tap what you get.

Last digit: 4^13

Last digit: 2^27

Last digit: 4^20