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Chapter 6 Exponents, Polynomials, and Polynomial Functions

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall 6.2 More Work with Exponents and Scientific Notation

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall 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 (ab) n = a n · b n Power rule(a m ) n = a mn Power of a product Power of a quotient

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Use the power rule to simplify the following expressions. Use positive exponents to write all results. a. (x 7 ) 2 = 2 9 = 512 = 2 3·3 Example b. (2 3 ) 3 c. (3 −1 ) 3 Solution a. (x 7 ) 2 = x 72 = x 14 b. (2 3 ) 3 c. (3 −1 ) 3 = 3 −13 = 3 −3

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Use the power rule to simplify the following expressions. Use positive exponents to write all results. = 5 3 · (x 2 ) 3 · y 3 = 125x 6 y 3 a. (5x 2 y) 3 Example a. (5x 2 y) 3 Solution

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Summary of Rules for Exponents If a and b are real numbers m and n are integers, then: Product rule a m · a n = a m+n Power rule (a m ) n = a mn Power of a product (ab) m = a m · b m Power of a quotient Quotient rule Zero exponent a 0 = 1 (a  0) Negative exponent

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Simplify each expression. Use positive exponents to write the answers. Example a. (4xy −4 ) −2 Solution a. (4xy −4 ) −2 = 4 −2 x −2 (y −4 ) −2 = 4 −2 x −2 y 8

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Simplify the expression. Use positive exponents to write the answer. Example Solution

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Simplify each expression. Assume that a and b are integers and that x and y are not 0. Example a. Solution a.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Perform the following operations. Write each result in scientific notation. = (7.3 · 8.1)  (10  2 · 10 5 ) = 59.13  10 3 = 59,130 (7.3  10  2 )(8.1  10 5 ) a. b. Example Solution (7.3  10  2 )(8.1  10 5 ) a. b.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Use scientific notation to simplify Write the result in scientific notation. Example Solution