Dividing Exponents

Home > Pre-Algebra > Exponents > 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}