Dividing exponents

Yesterday we learned that when you multiply exponents you add the number in the exponent, today we see that when you divide exponent you subtract the number in the exponent.

Consider

x⁷ / ³

What is this equal to?

x*x*x*x*x*x*x / x*x*x = x*x*x*x or x⁴

x⁷ / ³ = x^7-3 = x⁴

what about

x³ / ⁷

= 1 / x^7-3 = 1 / x⁴

We take the reciprocal because the exponent is greater in the divisor, or denominator.