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9.1 Exponents

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Practice Journal Page 174-177 (no calculators)

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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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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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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. 5353

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Write the power represented by the geometric model. x x

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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 MultiplicationPowerValueWords 3 3 3 3 3 3 3 3 3 3 3 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 3131 Reading Exponents 3232 3 3434 3535

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

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Use as a factor 2 times. 2929 Evaluate the expression. C. 2929 2929 = 4 81 2929 2929

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Evaluate each expression. a. (–5) 3 b. –6 2

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Evaluate the expression. c.

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Write each number as a power of the given base. A. 64; base 8 8 8 8282 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.

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Write each number as a power of a given base. a. 64; base 4 b. –27; base –3

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