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

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 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 1- 4 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Solution Multiply and simplify:

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 1- 6 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Solution Divide and simplify:

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 is undefined.)

Slide 1- 8 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Solution Evaluate each of the following for y = 5:

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 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Express using positive exponents and simplify if possible. Solution

Slide 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 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Write an equivalent expression without negative exponents: Solution

Slide Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example The product and quotient rules apply for all integer exponents. Solution Simplify:

Slide 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 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify: Solution

Slide 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 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify: Solution

Slide 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 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify: Solution