## Presentation on theme: "Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall."— Presentation transcript:

Chapter 8 Rational Exponents, Radicals, and Complex Numbers

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall 8.2 Rational Exponents

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Definition of a 1/n If n is a positive integer greater than 1 and is a real number, then

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Use radical notation to write the following. Simplify if possible. a. 81 1/4 b. (32x 10 ) 1/5 c. (16x 7 ) 1/3 Solution a. b. c.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall If m and n are positive integers greater than 1 with m/n in lowest terms, then as long as is a real number.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Use radical notation to write the following. Then simplify if possible. a.b.c. Solution a. b. c.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall as long as a m/n is a nonzero real number.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Write each expression with a positive exponent, and then simplify. a.b. Solution a. b.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Use properties of exponents to simplify. Write results with only positive exponents. a.b.c. Solution a. b. c.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Use properties of exponents to simplify. Write results with only positive exponents. a.b. Solution a. b.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Use rational exponents to simplify. Assume that variables represent positive numbers. a.b. Solution a. b.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Use rational exponents to write as a single radical. Solution