Eli5: Why is 2^9 + 2^9 = 2^10

Question

Middle school teacher here, and this is driving me crazy! Thanks!

In: 2

Answer 1

2^9 = 2*2*2*2*2*2*2*2*2. For any number x, x+x = 2*x, so 2^9 + 2^9 = 2*2^9 = 2*2*2*2*2*2*2*2*2*2 = 2^10.

For a similar reason, 3^9 + 3^9 + 3^9 = 3^10.