**Part 1**

1) Prove without a calculator that 4^{9} – 4^{8} is a multiple of 3.

2) Prove without a calculator that 9^{15} – 9^{14} is a multiple of 4.

3) Prove without a calculator that 2^{7} – 2^{5} is a multiple of 3.

4) Prove without a calculator that 5^{12} – 5^{10} is a multiple of 12.

**Part 2**

1) Prove that 18^{20} + 12^{11} is a multiple of 6.

2) Prove that 14^{89} + 21^{76} is a multiple of 7.

3) Prove that 5^{49} x 3^{41} is a multiple of 15.

4) Prove that 6^{93} x 4^{67} is a multiple of 12.