slide 1- 1 copyright © 2006 pearson education, inc. publishing as pearson addison-wesley

Download Slide 1- 1 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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Slide 1- 1 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2 Properties of Exponents The Product and Quotient Rules The Zero Exponent Negative Integers as Exponents Raising Powers to Powers Raising a Product or Quotient to a Power 1.6 Slide 3 Slide 1- 3 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Multiplying with Like Bases: The Product Rule For any number a and any positive integers m and n, (When multiplying powers, if the bases are the same, keep the base and add the exponents.) Slide 4 Slide 1- 4 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Solution Multiply and simplify: Slide 5 Slide 1- 5 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Dividing with Like Bases: The Quotient Rule For any nonzero number a and any positive integers m and n, m > n, (When dividing powers, if the bases are the same, keep the base and subtract the exponents.) Slide 6 Slide 1- 6 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Solution Divide and simplify: Slide 7 Slide 1- 7 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The Zero Exponent For any nonzero real number a, (Any nonzero number raised to the zero power is 1. 0 0 is undefined.) Slide 8 Slide 1- 8 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Solution Evaluate each of the following for y = 5: Slide 9 Slide 1- 9 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Negative Exponents For any real number a that is nonzero and any integer n, (The numbers a -n and a n are reciprocals of each other.) Slide 10 Slide 1- 10 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Express using positive exponents and simplify if possible. Solution Slide 11 Slide 1- 11 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Factors and Negative Exponents For any nonzero real numbers a and b and any integers m and n, (A factor can be moved to the other side of the fraction bar if the sign of the exponent is changed.) Slide 12 Slide 1- 12 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Write an equivalent expression without negative exponents: Solution Slide 13 Slide 1- 13 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example The product and quotient rules apply for all integer exponents. Solution Simplify: Slide 14 Slide 1- 14 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Raising a Power to a Power: The Power Rule For any real number a and any integers m and n, (To raise a power to a power, multiply the exponents.) Slide 15 Slide 1- 15 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify: Solution Slide 16 Slide 1- 16 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Raising a Product to a Power For any integer n, and any real numbers a and b for which (ab) n exists, (To raise a product to a power, raise each factor to that power.) Slide 17 Slide 1- 17 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify: Solution Slide 18 Slide 1- 18 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Raising a Quotient to a Power For any integer n, and any real numbers a and b for which a/b, a n, and b n exist, (To raise a quotient to a power, raise both the numerator and denominator to that power.) Slide 19 Slide 1- 19 Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify: Solution

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