# Exponent Rules

In these lessons, we will learn five rules of exponent and how to use them. These exponent rules are typically covered in Grade 7 Math.

The following table give the Exponent Rules. Scroll down the page for examples and solutions.

The rules of exponent are:

Product Rule:
When we multiply two powers that have the same base, add the exponents.
32 x 35 = 37

Power Rule:
When we raise a power to a power, multiply the exponents.
(32)5 = 310

Quotient Rule:
When we divide two powers with the same base, we subtract the exponents.
36 ÷ 32 = 34

Zero Rule:
Any nonzero number raised to the power of zero equals 1.
540 = 1

Negative Rule:
Any nonzero number raised to a negative power equals its reciprocal raised to the opposite positive power.
2-3 = 1/(23)

Introduction To Exponent Rules

Exponent Rules Song

Learn exponent rules through music!

Basic Exponent Properties

This video will illustrate the rules with a few examples.

Simple Rules Of When To Add Or Multiply The Exponents In Common Bases

Rules Of Exponents Set To Music

How To Apply The Rules Of Exponents?

Example:
Simplify the following expressions:
a) (2x34)(3xy5)2
b) (x5y9)(-5x2y2)4

Example:
Simplify the following expressions:
a) (x2/2)4
b) (4n6)2

Example:
Simplify the following expressions:
a) (3x2y4)5/(3x3y7)3
b) (5xy2)4/(5x2y)6

How To Evaluate Expressions With Negative Exponents?

Example:
Simplify the following expressions:
a) (8a6b-4)/(24a-8b9)
b) (10a2b6)(50a-3b-4)

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.