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Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 5.2 Negative Exponents and Scientific Notation

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2 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Negative Exponents Definition of a Negative Exponent where x 0

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3 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Write with positive exponents. a. b. Example

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4 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Negative Exponents Laws of Exponents Where x, y, ≠ 0 The Product Rule The Quotient Rule Power Rules Use if a > b. Use if a < b.

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5 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Negative Exponents Properties of Negative Exponents Where x, y, ≠ 0

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6 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Simplify. Write the expression with no negative exponents. a. b.

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7 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Scientific Notation A positive number is written in scientific notation if it is in the form a × 10 n, where 1 a 10 and n is an integer.

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8 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Scientific Notation 8200 = 8.2 1000 = 8.2 10 3 34,200,000 = 3.42 10000000 = 3.42 10 7 Greater than 1 and less than 10 Power of 10 Scientific notation

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9 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Write 67,300 in scientific notation. 67,300. = 6.73 10 n Starting position of decimal point Ending position of decimal point What power? The decimal point was moved 4 places to the left, so we use a power of 4. 67,300 = 6.73 10 4 A number that is larger than 10 and written in scientific notation will always have a positive exponent as the power of 10. Example

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10 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Write 0.048 in scientific notation. 0.048 = 4.8 10 n Starting position of decimal point Ending position of decimal point What power? The decimal point was moved 2 places to the right, so we use a power of –2. 0.048 = 4.8 10 –2 A number that is smaller than 1 and written in scientific notation will always have a negative exponent as the power of 10. Example

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11 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Write 9.1 10 4 in decimal notation. 9.1 10 4 = 9.1000 10 4 = 91,000 Write 6.72 10 –3 in decimal notation. 6.72 10 –3 = 6.72 10 –3 = 0.00672 Example Move the decimal point 4 places to the right. Move the decimal point 3 places to the left.

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12 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Use scientific notation and the laws of exponents to find the following. Leave your answer in scientific notation. Write each number in scientific notation. Rearrange the order. Multiply.

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13 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Use scientific notation and the laws of exponents to find the following. Leave your answer in scientific notation. Write each number in scientific notation. Rearrange the order. Rewrite with positive exponents.

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Simplify the following Write all the answers using positive exponents. 1) 4 0 = 1 4) = – 72) – 7w 0 3) 5)

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