Copyright 2006 Pearson Education Inc Publishing as Pearson

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

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

1. 6 Properties of Exponents n The Product and Quotient Rules n The Zero

1. 6 Properties of Exponents n The Product and Quotient Rules n The Zero Exponent n Negative Integers as Exponents n Raising Powers to Powers n Raising a Product or Quotient to a Power Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Multiplying with Like Bases: The Product Rule For any number a and any positive

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. ) Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 3

Example Multiply and simplify: Solution Copyright © 2006 Pearson Education, Inc. Publishing as Pearson

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

Dividing with Like Bases: The Quotient Rule For any nonzero number a and any

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. ) Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 5

Example Divide and simplify: Solution Copyright © 2006 Pearson Education, Inc. Publishing as Pearson

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

The Zero Exponent For any nonzero real number a, (Any nonzero number raised to

The Zero Exponent For any nonzero real number a, (Any nonzero number raised to the zero power is 1. 00 is undefined. ) Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 7

Example Evaluate each of the following for y = 5: Solution Copyright © 2006

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

Negative Exponents For any real number a that is nonzero and any integer n,

Negative Exponents For any real number a that is nonzero and any integer n, (The numbers a-n and an are reciprocals of each other. ) Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 9

Example Express using positive exponents and simplify if possible. Solution Copyright © 2006 Pearson

Example Express using positive exponents and simplify if possible. Solution Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 10

Factors and Negative Exponents For any nonzero real numbers a and b and any

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. ) Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 11

Example Write an equivalent expression without negative exponents: Solution Copyright © 2006 Pearson Education,

Example Write an equivalent expression without negative exponents: Solution Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 12

The product and quotient rules apply for all integer exponents. Example Simplify: Solution Copyright

The product and quotient rules apply for all integer exponents. Example Simplify: Solution Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 13

Raising a Power to a Power: The Power Rule For any real number a

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. ) Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 14

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

Example Simplify: Solution Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 15

Raising a Product to a Power For any integer n, and any real numbers

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. ) Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 16

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

Example Simplify: Solution Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 17

Raising a Quotient to a Power For any integer n, and any real numbers

Raising a Quotient to a Power For any integer n, and any real numbers a and b for which a/b, and bn exist, (To raise a quotient to a power, raise both the numerator and denominator to that power. ) Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 18

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

Example Simplify: Solution Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 19