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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

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

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Holt Algebra Powers and Exponents Evaluate expressions containing exponents. Objective

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Holt Algebra Powers and Exponents power base exponent Vocabulary

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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.

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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

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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

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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

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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

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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

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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.

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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.

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

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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.

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

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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

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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.

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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.

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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

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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

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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

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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

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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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