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Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.

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5.2 More Work with Exponents and Scientific Notation

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The Power Rule and Power of a Product or Quotient Rule for Exponents If a and b are real numbers and m and n are integers, then The Power Rule (ab) n = a n · b n Power Rule(a m ) n = a mn Power of a Product Power of a Quotient

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Simplify each of the following expressions. (2 3 ) 3 = 2 9 = 512 (x4)2(x4)2 = x 8 = 2 3·3 = x 4·2 Example = 5 3 · (x 2 ) 3 · y 3 = 125x 6 y 3 (5x 2 y) 3

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If m and n are integers and a and b are real numbers, then: Product rule for exponents a m · a n = a m+n Power rule for exponents (a m ) n = a mn Power of a product (ab) n = a n · b n Power of a quotient Quotient rule for exponents Zero exponent a 0 = 1, a ≠ 0 Negative exponent Summary of Exponent Rules

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Simplify each of the following expressions. Example

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Simplify by writing the following expression with positive exponents. Example

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Operations with Scientific Notation Multiplying and dividing with numbers written in scientific notation involves using properties of exponents.

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Example Perform the following operations. = (7.3 · 8.1) (10 -2 · 10 5 ) = 59.13 10 3 = 59,130 (7.3 10 -2 )(8.1 10 5 ) a. b.

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§ 5.5 Negative Exponents and Scientific Notation.

§ 5.5 Negative Exponents and Scientific Notation.

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