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

#### What if the base is different?

Answer:**Practice** Problems

Since we are multiplying exponents we add the exponents:

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

Use the power rule of exponents and multiply exponents:

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

Use the quotient rule of exponents and subtract the exponents:

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

Since we are multiplying exponents we add the exponents

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

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

#### Fraction Exponents

Fraction exponents are explained separately here