# 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.

Power

In words

Value

151

15 to the first power

151 = 15

(0.4)2

0.4 to the second power, or 0.4 squared

(0.4)(0.4) = 0.16

43

4 to the third power, or 4 cubed

⋅ 4 ⋅ 4 = 64

74

7 to the fourth power

⋅ 7 ⋅ 7 ⋅ 7 = 2401

## 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 :

 a.  154 The base 15 is used as a factor 4 times.
 b.  (0.5)3 The base 0.5 is used as a factor 3 times.
 c.  x6 The base x is used as a factor 6 times.
 d.  y5 The base y is used as a factor 5 times.

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. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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