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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 242^4.

We can also look at it like this:

2622=22222222=22222222=24=16dfrac{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)

x2x5\dfrac{x^{2}}{x^{5}}
When dividing exponents with like bases, you subtract the exponents
x2x5\dfrac{x^{2}}{x^{5}}
x25x^{2-5}

Dividing Exponents (Example #2)

2423\dfrac{2^{4}}{2^{3}}
When dividing exponents with like bases, you subtract the exponents
2423\dfrac{2^{4}}{2^{3}}
2432^{4-3}

Dividing Exponents (Example #3)

8685\dfrac{8^{6}}{8^{5}}
When dividing exponents with like bases, you subtract the exponents
8685\dfrac{8^{6}}{8^{5}}
8658^{6-5}

Dividing Exponents Worksheets (PDF)

Dividing Exponents Worksheet 1

Dividing Exponents Worksheet 2

Dividing Exponents Worksheet 3

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