What is the unit digit of $3^{65} \times 7^{42}$?

Explanation

1. 01

   Powers of 3 end in 3, 9, 7, 1; $65 \div 4$ leaves 1, so the unit digit is 3.

2. 02

   Powers of 7 end in 7, 9, 3, 1; $42 \div 4$ leaves 2, so the unit digit is 9.

3. 03

   $3 \times 9 = 27$, so the unit digit is 7.