Picture of Exponent and BaseLaws of Exponents

How to simplify expressions using the laws of exponents

There are many different laws of exponents. This page covers the 3 most frequently studied formulas in Algebra I. If you are looking for other laws, visit our exponents home page.

Video on the Laws of Exponents

Rules and Laws Covered on This Page

Examples

Division: Exponent Formula Picture Example of rule 2
Exponent to an exponent:

What if the base is different?

Answer: different bases

Practice Problems

Problem 1

Simplify $ x^3 \times x^2 $

Since we are multiplying exponents we add the exponents:

$ x^3 \times x^2 = x^{3+2} = x^5 $

Problem 2

Simplify $ (x^3) ^2 $

Use the power rule of exponents and multiply exponents:

$ (x^3) ^2 = x^{(3 \times 2)}= x^6 $

Problem 3

Evaluate $ \frac {x^5}{ x^3} $

Use the quotient rule of exponents and subtract the exponents:

$ \frac {x^5}{ x^3} = x^{(5 - 3)}= x^2 $

Problem 4

Simplify $ x^{11} \times x^5 $

Since we are multiplying exponents we add the exponents

$ x^{11} \times x^5 = x^{11+5} = x^{16} $

Problem 5

Simplify $ x^8 \times y^5 $

You cannot simplify this expression! Remember that all of the rules on this page only work when the exponents have the same base!

Rules and Laws Covered elsewhere

Negative Exponents


Negative exponents are explained separately here.


Fraction Exponents

Fraction exponents are explained separately here


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