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## Dividing Exponents

#### Introduction

Dividing exponents is quite straightforward. When the bases are the same, we simply subtract the denominator (bottom) exponent from the numerator (top) exponent.

#### Terms

Exponent - The number of times to multiply the base.
Base - The number being multiplied.

## Lesson

To divide exponents with the same base, we subtract the bottom exponent from the top exponent. For example, if we are given , we subtract the exponents – 6-2=4 and we are left with $2^4$.

We can also look at it like this:

$dfrac{2^6}{2^2} = dfrac{2*2*2*2*2*2}{2*2} = dfrac{2*2*2*2*2*2}{2*2} = 2^{4} = 16$

## Examples

#### Dividing Exponents (Example #1)

$\dfrac{x^{2}}{x^{5}}$
When dividing exponents with like bases, you subtract the exponents
$\dfrac{x^{2}}{x^{5}}$
$x^{2-5}$

#### Dividing Exponents (Example #2)

$\dfrac{2^{4}}{2^{3}}$
When dividing exponents with like bases, you subtract the exponents
$\dfrac{2^{4}}{2^{3}}$
$2^{4-3}$

#### Dividing Exponents (Example #3)

$\dfrac{8^{6}}{8^{5}}$
When dividing exponents with like bases, you subtract the exponents
$\dfrac{8^{6}}{8^{5}}$
$8^{6-5}$