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Holt Algebra 1

1-4 Powers and Exponents1-4 Powers and Exponents

Holt Algebra 1

Warm Up

Lesson Presentation

Lesson Quiz

Holt Algebra 1

1-4 Powers and Exponents

Warm Up

Simplify.

1. 2(2)

2. (–2)(–2)

3. (–2)(–2)(–2)

4. 3(3)(3)

4

4

–8

27

4 9

5.

Holt Algebra 1

1-4 Powers and Exponents

Evaluate expressions containing exponents.

Objective

Holt Algebra 1

1-4 Powers and Exponents

power

base

exponent

Vocabulary

Holt Algebra 1

1-4 Powers and Exponents

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 the

number that is used as a factor.

32 The exponent, 2 tells

how many times the base, 3, is used as a factor.

Holt Algebra 1

1-4 Powers and Exponents

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 its “cubed.” The of volume of a cube is s s s = s3 is the side length.

S

S S

Holt Algebra 1

1-4 Powers and Exponents

Write the power represented by the geometric model.

5 5

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

1-4 Powers and Exponents

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

1-4 Powers and Exponents

Write the power represented by each geometric model.

a.

22

b.

Check It Out! Example 1

x

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

Holt Algebra 1

1-4 Powers and Exponents

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

1-4 Powers and Exponents

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

1-4 Powers and Exponents

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 and

two 10’s.

Example 2: Evaluating Powers

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

Holt Algebra 1

1-4 Powers and Exponents

Use as a factor 2 times.2 9

Evaluate the expression.

C.

2 9

2 9

Example 2: Evaluating Powers

= 4

81 2 9

2 9

Holt Algebra 1

1-4 Powers and Exponents

Evaluate each expression.

a. (–5)3

b. –62

Check It Out! Example 2

(–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 and two 6’s.

Holt Algebra 1

1-4 Powers and Exponents

Check It Out! Example 2

Evaluate the expression.

c.

Use as a factor 3 times.3 4

27 64

Holt Algebra 1

1-4 Powers and Exponents

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

1-4 Powers and Exponents

Write each number as a power of a given base.

a. 64; base 4

b. –27; base –3

Check It Out! Example 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

1-4 Powers and Exponents

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

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

Example 4: Problem-Solving Application

Understand the problem1

List the important information:

• The PTA president calls 3 families.

• Each family then calls 3 more families.

Holt Algebra 1

1-4 Powers and Exponents

Draw a diagram to show the number of

Families called in each round of calls.

2 Make a Plan

Example 4 Continued

2nd round of calls

1st round of calls

PTA President

Holt Algebra 1

1-4 Powers and Exponents

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 have

been 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

Solve3

Example 4 Continued

Holt Algebra 1

1-4 Powers and Exponents

Drawing a diagram helps you visualize the

problem, but the numbers become too large for a diagram. The diagram helps you recognize the pattern of multiplying by 3 so that you can write the number as a power of 3.

Look Back4

Example 4 Continued

Holt Algebra 1

1-4 Powers and Exponents

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

Check it Out! Example 4

28 After 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

1-4 Powers and Exponents

1. Write the power represented by the geometric model.

n

n n 2

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