Question

Explain why you can subtract exponents when you are dividing two powers with the same base.

Answer 1

To divide exponents (or powers) with the same base, subtract the exponents. Division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.

Answer 2

When you divide numbers, you make the value smaller.  So subtract the exponents will make the value with that base smaller.