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Warm Up Evaluate. 27 1. 3 3 2. 4 4 4 4 3. b 2 for b = 4 4. n 2 r for n = 3 and r = 2 256 16 18

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Lesson 4.3: Powers of Exponents

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Objectives Multiply, divide, and simplify rational numbers by using exponent rules (NS 2.3). Understand negative whole-number exponents. (NS 2.1)

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Parts of a power Parts of a power A power has two parts: a base and an exponent. Baserepresents the repeated factor in the product Exponent represents the number of times the base is repeated as a factor in the product. Base Exponent Factors =a●a●a●a a4a4 Read, “a to the forth power.”

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Multiplying Powers with the same base (a ●a ● a ● a ●a) ●(a ● a ● a) a 5 ●a 3 = 5 factors 3 factors 8 factors = a 8 Notice: The exponent of a is 8, which is equal to 5 + 3.

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a) 2 2 2 2 b) x9 x c) 3 6 3 -2 = 22+2= 24 = 16 = x9+1 =x10 1 = 36+-2 = 34 = 81 Rule #1When multiplying powers with the same base, ADD the exponents. Rule #1: When multiplying powers with the same base, ADD the exponents. a m a n = a m + n

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1 Now you try.

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2x 2 3x 4 Using repeated multiplication Using exponent rule = (2 x x) (3 x x x x) = 6x 6 = (2 3) (x 2 x 4 ) = 6x 2 + 4 a m a n = a m + n Multiplying Variable Expressions

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Simplify. Simplifying Variable Expressions

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Raising a Power with a Power A. (5 4 ) 2 (5 4 ) 2 5 4 2 5858 B. (6 7 ) 9 (6 7 ) 9 6 7 9 6 63 Simplify each expression. Write your answer in exponential form. C. D. (17 2 ) –20 17 2 –20 17 –40 2323 12 –3 2323 –36 Multiply exponents.

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c5c5 c3c3 = c c c c c c c c 111 111 3 copies of c 5 copies of c Dividing Powers with the same base =c c=c 2 Notice: The exponent of c is 2, which is equal to 5-3

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Rule #2 Rule #2: When dividing powers with the same base, SUBTRACT the exponents of the denominator from the exponent of the numerator. amam anan = a m - n 2525 2323 = 2 5 - 3 a) b) 8x 8 4x 3 = 2x 8 - 2 = 2 2 = x 6 x5y4x5y4 x3yx3y = x 5 -3 y 4-1 =x 2 y 3 c)

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Now you try

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Summary When multiplying powers with the same base, keep the base and add the exponents. When dividing powers with the same base, keep the base and subtract the exponents.

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Lesson Quiz 3. 8 9 n 7 1. n 3 n 4 10 9 10 5 10 4 4. t 2 5. 3 2 3 3 3 5 3 10 2. 8 8 8 t 9 t 7 6. (m 2 ) 19 m 38 7. (9 -8 ) 9 8. (10 4 ) 0 1 Simplify each expression. Write your answer in exponential form. 1 9 72

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