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

Because adding 1 to the exponent is the same as multiplying by the base, which in this case is 2.

This won’t work for other bases. E.g. 3^9 + 3^9 is not 3^10.