Copyright 2006 Pearson Education Inc Publishing as Pearson
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 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 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 Addison-Wesley Slide 1 - 4
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 Addison-Wesley Slide 1 - 6
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 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, (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 Education, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 10
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, Inc. Publishing as Pearson Addison-Wesley Slide 1 - 12
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 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 1 - 15
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 1 - 17
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 1 - 19
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