Holt Algebra 1 1-4 Powers and Exponents 1-4 Powers and Exponents Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson

Holt Algebra 1

1-4 Powers and Exponents1-4 Powers and Exponents

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt Algebra 1

1-4 Powers and Exponents

Warm UpSimplify.1. 2(2) 2. (–2)(–2)

3. (–2)(–2)(–2)

4. 3(3)(3)

4

4

–8

27

495.

Holt Algebra 1


Evaluate expressions containing exponents.

Objective

Holt Algebra 1


powerbaseexponent

Vocabulary

Holt Algebra 1


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

The base is thenumber that isused as a factor.

32 The exponent, 2 tellshow many times thebase, 3, is used as afactor.

Holt Algebra 1


When a number is raised to the second power, we usually say it is “squared.” The area of a square is s s = s2, is the side length.

S

S

When a number is raised to the third power, we usually say it is “cubed.” The of volume of a cube is s s s = s3 is the side length.

S

SS

Holt Algebra 1


Write the power represented by the geometric model.

55

5 The figure is 5 units long, 5 units wide, and 5 units tall. 5 5 5

The factor 5 is used 3 times.53

Example 1A: Writing Powers for Geometric Models

Holt Algebra 1


Write the power represented by the geometric model.

The figure is 6 units long and 6 units wide. 6 x 6

The factor 6 is used 2 times.62

6

6

Example 1B: Writing Powers for Geometric Models

Holt Algebra 1


Write the power represented by each geometric model.

a.

22

b.

Check It Out! Example 1

x

x

The figure is 2 units long and 2 units wide. 2 2

The factor 2 is used 2 times.

The figure is x units long, x units wide, and x units tall. x x x

The factor x is used 3 times.x3

x

Holt Algebra 1


There are no easy geometric models for numbers raised to exponents greater than 3, but you can still write them using repeated multiplication or a base and exponent.

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

Reading Exponents

32

33

34

35

Holt Algebra 1


Caution!In the expression –52, 5 is the base because

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

Holt Algebra 1


Evaluate each expression.

A. (–6)3

(–6)(–6)(–6)

–216

B. –102

–1 • 10 • 10

–100

Use –6 as a factor 3 times.

Find the product of –1 andtwo 10’s.

Example 2: Evaluating Powers

Think of a negative sign in front of a power as multiplying by a –1.

Holt Algebra 1


Use as a factor 2 times.2 9

Evaluate the expression.

C.

29

29

Example 2: Evaluating Powers

= 4

81

29

29

Holt Algebra 1


Evaluate each expression.

a. (–5)3

b. –62


(–5)(–5)(–5) Use –5 as a factor 3 times.

–125

–1 6 6

–36

Think of a negative sign in front of a power as multiplying by –1.

Find the product of –1 andtwo 6’s.

Holt Algebra 1



Evaluate the expression.

c.

Use as a factor 3 times.34

2764

Holt Algebra 1


Write each number as a power of the given base.

A. 64; base 8

8 8

82

B. 81; base –3

(–3)(–3)(–3)(–3)

(–3)4

The product of two 8’s is 64.

The product of four –3’s is 81.

Example 3: Writing Powers

Holt Algebra 1


Write each number as a power of a given base.

a. 64; base 4

b. –27; base –3


4 4 4 The product of three 4’s is 64.

43

(–3)(–3)(–3)

–33

The product of three (–3)’s is –27.

Holt Algebra 1


In case of a school closing, the PTApresident calls 3 families. Each of these families calls 3 other familiesand so on. How many families will have been called in the 4th round of calls?

The answer will be the number of familiescontacted in the 4th round of calls.

Example 4: Problem-Solving Application

Understand the problem11

List the important information:

• The PTA president calls 3 families.• Each family then calls 3 more families.

Holt Algebra 1


Draw a diagram to show the number of Families called in each round of calls.

22 Make a Plan

Example 4 Continued

2nd round of calls

1st round of calls

PTA President

Holt Algebra 1


Notice that after each round of calls the number of families contacted is a power of 3.

1st round of calls: 1 3 = 3 or 31 families contacted

So, in the 4th round of calls, 34 families will havebeen contacted.

34 = 3 3 3 3 = 81

Multiply four 3’s.

In the fourth round of calls, 81 families will have been contacted.

2nd round of calls: 3 3 = 9 or 32 families contacted

3rd round of calls: 9 3 = 27 or 33 families contacted

Solve33

Example 4 Continued

Holt Algebra 1


Drawing a diagram helps you visualize the problem, but the numbers become toolarge for a diagram. The diagram helps you recognize the pattern of multiplying by 3 so that you can write the number as apower of 3.

Look Back44

Example 4 Continued

Holt Algebra 1


What if…? How many bacteria will be on the slide after 8 hours?

Check it Out! Example 4

28After each hour, the number of bacteria is a power of 2.

2 2 2 2 2 2 2 2 Multiply eight 2’s.

The product of eight 2’s.256

Holt Algebra 1


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

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Holt Algebra 1 1-4 Powers and Exponents 1-4 Powers and Exponents Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson