Warm Up

Simplify.

1. -20 ÷ (2)

2. (–2)(–2)

3. (–2)(–2)(–2)

4. -3(3)(-3)

-10

4

–8

27

4

95.

Section 1.4

Powers and Exponents

Objectives

• Interpret and evaluate expressions involving powers. (AF2.0)

• Interpret positive whole number powers as repeated multiplication. (AF2.1)

• Use formulas for finding the area and volume of basic figures. (MG2.1)

Words to Know

• Power

– an expression written with an exponent and a base or the value of such an expression. 3² is an example of a power.

• Base

– The base, 3, is the number that is used as a factor.

• Exponent

– The exponent, 2, tells how many times the base, 3, is used as a factor.

23 = 2 • 2 • 2 = 8

3 to the second power, or 3 squared

3 3 3 3 3

Multiplication Power ValueWords

3 3 3 3

3 3 3

3 3

33 to the first power

3 to the third power, or 3 cubed

3 to the fourth power

3 to the fifth power

3

9

27

81

243

31

32

33

34

35

Reading Exponents

Reading a PowerPower Verbal

PhraseRepeated

Multiplication

Caution!

In the expression –5², 5 is the base because the negative sign is not in parentheses. In the expression (–2)³, –2 is the base because of the parentheses.

Rewrite each power as repeated multiplication and evaluate

• 42 =

• 34 =

• 103 =

4 • 4 = 16

3 • 3 • 3 • 3 = 81

10 • 10 • 10 = 1000

Now you try…

• 2 9 =

• 3 4 =

• 7 3 =

• 5 4 =

• 8 3 =

• 10 5 =

Area and Volume

AREA of a SQUAREA = s2

A = 32 A = 3 • 3A = 9 units

Volume of a Cube

V = s3

V = 33

V = 3 • 3 • 3

V = 27 units

Simplify the following if x = 4

• x2 =

• 2x =

• x2 • x =

42 = 4 • 4 = 16

24 = 2 • 2 • 2 • 2 = 16

42 • 4 = 16 • 4 = 64

Use as a factor 2 times.2 9

Simplify the expression.

2

9 2

9

Evaluating Powers

= 4

81

2

9 2

9

1. Write the power represented by the geometric model.

n

n n2

Simplify each expression.

2.

4. 6

3. –63

5. (–2)6

−216

216 64

Lesson Quiz

Write each number as a power of the given base.

6. 343; base 7 7. 10,000; base 1073 104