What is the unit digit of $7^{23}$?

Explanation

1. 01

   Unit digits of powers of 7 repeat in a cycle of 4: 7, 9, 3, 1.

2. 02

   $23 \div 4$ leaves remainder 3.

3. 03

   So $7^{23}$ has the same unit digit as $7^3$, which is 3.