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Exponents

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What number is being multiplied over and over again? 5 5 5 How many times is 5 used as a factor?

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The base is the number being multiplied. The exponent is the number of times the number is a factor. 5 5 5 5 5 5 = 5 6 Identify the base and the exponent in 5 6.

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Multiplying Powers with the Same Base To multiply powers with the same base, add the exponents. 5 4 5 2 = 5 (4 + 2) = 5 6 5 5 5 5 5 5 = 5 6

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Dividing Powers with the Same Base To divide powers with the same base, subtract the exponents. 5 5 5 5656 5 6 ÷ 5 4 = == 52= 52 5 5 5454 Case 1 — result has a positive exponent 5 6 ÷ 5 4 = 5 (6 – 4) = 5 2

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Dividing Powers with the Same Base To divide powers with the same base, subtract the exponents. Case 2 — result has a negative exponent 5 4 ÷ 5 6 = 5 (4 – 6) = 5 –2 5 5 5 5454 5 4 ÷ 5 6 = == 5 –2 5 5 5656 1 5252 =

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Dividing Powers with the Same Base To divide powers with the same base, subtract the exponents. Case 3 — result has an exponent of 0 5 4 ÷ 5 4 = 5 (4 – 4) = 5 0 = 1 5 5 5454 5 4 ÷ 5 4 = = 5 5 5454 = 1

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Power to a Power To raise a power to a power, multiply the exponents. (5 4 ) 2 = (5 5 5 5)(5 5 5 5) = 5 8 (5 4 ) 2 = 5 (4 2) = 5 8

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Product to a Power To raise a product to a power, raise each factor to the power and then multiply. Or, you can find the product first, and then raise to the power. (4 6) 2 = 4 2 6 2 = 16 36 = 576 (4 6) 2 = 24 2 = 24 24 = 576

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Quotient to a Power To raise a quotient to a power, raise the numerator and denominator to the power and then divide. 22 2 2w 2 x y3y3 4 = 2 4 w (2 x 4) x (4) y (3x4) = 16w 8 x 4 y 12

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