Large-Exponent Cycles

Find the last digit of huge powers like 7^100

Last digit of 7^100 = 1

Powers of 7 walk the same ring of four, however large the exponent gets.

100 is exactly 25 laps of 4, with no steps left over at the end.

A whole number of laps finishes on the last stop, so 7¹⁰⁰ ends in 1.

Your turn

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

Last digit: 4^168

Last digit: 7^149

Last digit: 8^69