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.




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

Exponent Rules

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)



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