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.

Exponent

Exponents tell you how many times a factor is multiplied.

x * x * x (x times x times x)

Can be written as x³ or x^3 , when we write the multiplication in this way, we call it an exponent.

To multiply exponents we add them, for example, consider we have

x² * x³

what is this equal to?

x⁵

why is this? Well if we write it out, it becomes obvious


x² * x³

=


(x*x) * (x*x*x) or x⁵

if we have

5x² * 2x³

Then the bottom numbers (or base numbers) are multiplied, while the exponents are added


5x² * 2x³
=
10x⁵