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Rules of Exponents

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Introduction Product Rule—when multiplying with the same base, add exponents. Quotient Rule—when dividing with the same base, subtract exponents. Power Rule—when raising a power to a power, multiply exponents.

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Goal: Multiply Powers To multiply powers with the same base, add their exponents. a m a n = a m + n

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Guided Practice Find the product. Write your answer using exponents. 4 7 4 11 4 7 + 11 = 4 18 2 5 2 12 2 5 + 12 = 2 17 5 6 5 2 5 3 5 6 + 2 + 3 = 5 11 x 6 x 13 x 6 + 13 = x 19 b 2 b 4 b b 2 + 4 + 1 = b 7 2x 2 7x 6 2 7 x 2 + 6 14x 8

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Independent Practice Find the product. Write your answer using exponents. 1. 5 10 5 11 2. 4 8 4 9 3. 5 4 5 3 4. n 8 n 9 5. y 10 y 12 6. (-a) 8 (-a) 9 7. 6 7 6 2 6 8 8. d 4 d 8 9. 3h 5 4h 6 10. 5g 2 g 16

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Goal: Divide Powers To divide powers with the same base, subtract their exponents. a m = a m - n a n

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Guided Practice Find the quotient. Write your answer using exponents. 4 11 4 7 4 11 – 7 = 4 4 2 12 2 5 2 12 – 5 = 2 7 x 9 x 3 x 9 – 3 = x 6 x 13 x 3 x 13 – 3 = x 10 b 4 b b 4 – 1 = b 3 35x 6 7x 2 35 7 x 6 –2 5x 4

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Independent Practice Find the quotient. Write your answer using exponents. 1. 4 9 4 7 2. 2 12 2 5 3. x 9 x 3 4. x 13 x 3 5. y 20 y 12 6. b 4 b 7. 49x 5 7x 2 8. 25x 6 5x 9. 36x 8 9x 3

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Goal: Raise a power to a power To raise a power to a power, multiply their exponents. (a m ) n = a m n

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Guided Practice Find the power. Write your answer using exponents. (4 7 ) 11 4 7 11 = 4 77 (2 5 ) 12 2 5 12 = 2 60 (5 6 ) 2 5 6 2 = 5 12 (x6)3 (x6)3 (x6)3 (x6)3 x 6 3 = x 18 (b 2 ) -4 b 2 -4 = b -8 = 1/b 8 (x -2 ) -3 x -2 -3 = x 6

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Independent Practice Find the power. Write your answer using exponents. 1. (5 10 ) 2 2. (4 8 ) 3 3. (5 4 ) 3 4. (n 8 ) 2 5. (y 10 ) -2 6. (a -5 ) -8 7. (6 7 ) 8 8. (d 4 ) -8 9. (h -5 ) -6 10. (g 2 ) 16

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Summary Product Rule—when multiplying with the same base, add exponents. Quotient Rule—when dividing with the same base, subtract exponents. Power Rule—when raising a power to a power, multiply exponents.

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