POWERS AND EXPONENTS

A power is the result of a repeated multiplication of the same factor. 

For example, 125 is 5 to the 3rd power. Because

125  =  5 ⋅ 5 ⋅ 5

A power can be written in a form that has two parts. 

A number called the base and a number called the exponent. The exponent shows the number of times the base is used a factor. 

Number raised to the first power, such as 13¹, are usually written without the exponent. 

We can read and write powers as given below. 

Using Exponents

Example 1 : 

Write the following products using an exponent. 

a.  15 ⋅ 15 ⋅ 15 ⋅ 15 

b.  (0.5)(0.5)(0.5) 

c.  x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x

d.  y ⋅ y ⋅ y ⋅ y ⋅ y

Solution : 

Example 2 : 

Evaluate the expression m⁵ when m = 3. 

Solution : 

=  m⁵

Substitute 3 for m.

=   (3)⁵

Use 3 as a factor 5 times. 

=  3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3

Multiply. 

=  243

Example 3 : 

Evaluate the expression x⁴ when x = 0.5. 

Solution : 

=  x⁴

Substitute 0.5 for x.

=   (0.5)⁴

Use 0.5 as a factor 4 times. 

=   (0.5)(0.5)(0.5)(0.5)

Multiply. 

=  0.0625

Use Powers in Formulas

Example 4 : 

An artist uses a cube-shaped block of ice to make an ice sculpture for a competition. Find the volume of the block of ice. 

Solution : 

Use the formula for volume of a cube :

V  =  s³

Substitute 15 for s. 

=  15³

Use 15 as a factor 3 times. 

=  15 ⋅ 15 ⋅ 15

Multiply. 

=  3375

The volume of the block of ice is 3375 cubic inches.  

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