Sometimes you're asked to find the unit digit of $n^x$, where $x$ is so large that if you tried to put it into your calculator, it would explode. Thus, you should memorize or be able to figure out the Exponent Unit Digit Patterns.

$0^n$: always $0$
$1^n$: always $1$
$2^n$: $2, 4, 8, 6$, $2,4,8,6$ and so on
- repeats in blocks of $4$
$3^n$: $3, 9, 7, 1$, $3,9,7,1$ and so on
- repeats in blocks of $4$
$4^n$: $4, 6$, $4, 6$, $4, 6$ and so on
- repeats in blocks of $2$
$5^n$: always $5$
$6^n$: always $6$
$7^n$: $7, 9, 3, 1$, $7, 9, 3, 1$ and so on
- repeats in blocks of $4$
$8^n$: $8, 4, 2, 6$, $8, 4, 2, 6$ and so on
- repeats in blocks of $4$
$9^n$: $9, 1$, $9, 1$, $9, 1$ and so on
- repeats in blocks of $2$