What is the unit digit of $7^{95} - 3^{58}$?

Explanation

1. 01

   Powers of 7 end in 7, 9, 3, 1; $95 \div 4$ leaves 3, so the unit digit is 3.

2. 02

   Powers of 3 end in 3, 9, 7, 1; $58 \div 4$ leaves 2, so the unit digit is 9.

3. 03

   $7^{95}$ is far larger than $3^{58}$, so subtracting means borrowing: $13 - 9 = 4$.