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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.

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Presentation on theme: "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."— Presentation transcript:

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

2 Holt Algebra Powers and Exponents Warm Up Simplify. 1. 2(2) 2. (–2)(–2) 3. (–2)(–2)(–2) 4. 3(3)(3) 4 4 –

3 Holt Algebra Powers and Exponents Evaluate expressions containing exponents. Objective

4 Holt Algebra Powers and Exponents power base exponent Vocabulary

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

6 Holt Algebra 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 = s 2, 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 = s 3 is the side length. S S S

7 Holt Algebra Powers and Exponents Write the power represented by the geometric model The figure is 5 units long, 5 units wide, and 5 units tall The factor 5 is used 3 times Example 1A: Writing Powers for Geometric Models

8 Holt Algebra 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 Example 1B: Writing Powers for Geometric Models

9 Holt Algebra Powers and Exponents Write the power represented by each geometric model. a. 2 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. x3x3 x

10 Holt Algebra 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 MultiplicationPowerValueWords to the first power 3 to the third power, or 3 cubed 3 to the fourth power 3 to the fifth power Reading Exponents

11 Holt Algebra Powers and Exponents Caution! In the expression –5 2, 5 is the base because the negative sign is not in parentheses. In the expression (–2), –2 is the base because of the parentheses.

12 Holt Algebra Powers and Exponents Evaluate each expression. A. (–6) 3 (–6)(–6)(–6) –216 B. –10 2 – –100 Use –6 as a factor 3 times. Find the product of –1 and two 10s. Example 2: Evaluating Powers Think of a negative sign in front of a power as multiplying by a –1.

13 Holt Algebra Powers and Exponents Use as a factor 2 times Evaluate the expression. C Example 2: Evaluating Powers =

14 Holt Algebra Powers and Exponents Evaluate each expression. a. (–5) 3 b. –6 2 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 6s.

15 Holt Algebra Powers and Exponents Check It Out! Example 2 Evaluate the expression. c. Use as a factor 3 times

16 Holt Algebra Powers and Exponents Write each number as a power of the given base. A. 64; base B. 81; base –3 (–3)(–3)(–3)(–3) (–3) 4 The product of two 8s is 64. The product of four –3s is 81. Example 3: Writing Powers

17 Holt Algebra 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 The product of three 4s is (–3)(–3)(–3) –3 3 The product of three (–3)s is –27.

18 Holt Algebra 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 4 th round of calls? The answer will be the number of families contacted in the 4 th round of calls. Example 4: Problem-Solving Application Understand the problem 1 List the important information: The PTA president calls 3 families. Each family then calls 3 more families.

19 Holt Algebra 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 2 nd round of calls 1 st round of calls PTA President

20 Holt Algebra Powers and Exponents Notice that after each round of calls the number of families contacted is a power of 3. 1 st round of calls: 1 3 = 3 or 3 1 families contacted So, in the 4 th round of calls, 3 4 families will have been contacted. 3 4 = = 81 Multiply four 3s. In the fourth round of calls, 81 families will have been contacted. 2 nd round of calls: 3 3 = 9 or 3 2 families contacted 3 rd round of calls: 9 3 = 27 or 3 3 families contacted Solve 3 Example 4 Continued

21 Holt Algebra 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

22 Holt Algebra Powers and Exponents What if…? How many bacteria will be on the slide after 8 hours? Check it Out! Example After each hour, the number of bacteria is a power of Multiply eight 2s. The product of eight 2s. 256

23 Holt Algebra Powers and Exponents 1. Write the power represented by the geometric model. n n n2n2 Simplify each expression – (–2) Lesson Quiz Write each number as a power of the given base ; base ,000; base


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