why do you subtract exponents when dividing power with the same base?

Question

 explain it

Answer 1

10^x / 10^y, x ≥ y

If you reduce this fraction all "y" of the factors of the denominator are reduce with "y" of the factors in the numerator.

What is left in the numerator is "x - y" factors.

Answer 2

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

 

100 / 10 = 10

 

10² / 10¹ = 10¹ = 10