Definitions:Exponent – Is the number that tells us how many times to multiply a number (called the base) by itself.Base – Is a number that is multiplied by itself when it is raised to an exponent.

Exponential Form – Is the form of a number when it is written with a base and an exponent.Perfect Squares – Are numbers that are the squares of whole numbers. For example, 81 is a perfect square because it is the value of 92.

Exponent

Base 45

Exponents

Exponential Form

Read Multiply Value

101 Ten to the first power --- 10

102 Ten to the second power or ten squared

10 x 10 100

103

104

Exponents

Writing Numbers in Exponential Form

Example 1

7 x 7 x 7 = 73

Example 2

5 x 5 x 5 x 5 = 54

Try these: Write the following expressions in exponential form.

1.) 6 x 6 = 2.) 10 x 10 x 10 x 10 =

3.) 2 x 2 x 2 x 2 x 2 = 4.) 12 x 12 x 12 =

Exponents

Finding the Value of Numbers Written in Exponential Form

Example 1

83 = 8 x 8 x 8 = 512

Example 2

Try these: Find the value of the following numbers written in exponential form.

1.) 94 = 2.) 15 =

3.) 4.12 = 4.)

8

1

2

1

2

1

2

1

2

13

3

3

2

Exponents

Comparing Exponents

Example 1

101 __ 22

10 __ 2 x 2

10 _>_ 4

Try these: Compare the following numbers written in exponential form. Then, place a <, > or = sign between them.

1.) 82 __ 43 2.) 251 __ 53

Evaluate the exponents

Place the correct sign between the two numbers

Example 2

43 __ 53

4 x 4 x 4 __ 5 x 5 x 5

64 _<_ 125

Evaluate the exponents

Place the correct sign between the two numbers

Exponents

Real-Life Application

The zoo has an aquarium that holds 74 cubic gallons of water. How many gallons of water does the aquarium hold?

Exponents