1. Copyright © 2007 Pearson Education, Inc. Slide R-1

2. Copyright © 2007 Pearson Education, Inc. Slide R-2 Chapter R: Reference: Basic Algebraic Concepts R.1Review of Exponents and Polynomials R.2Review of Factoring R.3Review of Rational Expressions R.4Review of Negative and Rational Exponents R.5Review of Radicals

3. Copyright © 2007 Pearson Education, Inc. Slide R-3 R.4 Review of Negative and Rational Exponents Negative Exponent If a is a nonzero real number and n is any integer, then

4. Copyright © 2007 Pearson Education, Inc. Slide R-4 R.4 Using the Definition of a Negative Exponent Example Evaluate. (a) (b)(c) Solution (a) (b) (c)

5. Copyright © 2007 Pearson Education, Inc. Slide R-5 R.4 Review of Negative and Rational Exponents Example Write without a negative exponent. (a) (b) Solution (a) (b)

6. Copyright © 2007 Pearson Education, Inc. Slide R-6 R.4 Review of Negative and Rational Exponents Quotient Rule For all integers m and n and all nonzero real numbers a,

7. Copyright © 2007 Pearson Education, Inc. Slide R-7 R.4 Using the Quotient Rule Example Simplify each expression. Assume variables represent nonzero numbers. (a) (b) Solution (a) (b)

8. Copyright © 2007 Pearson Education, Inc. Slide R-8 R.4 Rational Exponents a 1/n n even If n is an even positive integer, and if a > 0, then a 1/n is the positive real number whose nth power is a. That is, n odd If n is an odd positive integer and if a is any real number, then a 1/n is the positive or negative real number whose nth power is a. That is,

9. Copyright © 2007 Pearson Education, Inc. Slide R-9 R.4 Using the Definition of a 1/n Example Evaluate each expression. (a) (b)(c) Solution (a) (b)(c)

10. Copyright © 2007 Pearson Education, Inc. Slide R-10 R.4 Rational Exponents Rational Exponent For all integers m, all positive integers n, and all real numbers a for which a 1/n is a real number,

11. Copyright © 2007 Pearson Education, Inc. Slide R-11 R.4 Using the Definition of a m/n Example Evaluate each expression. (a) (b) (c)(d) Solution (a) (b)

12. Copyright © 2007 Pearson Education, Inc. Slide R-12 R.4 Using the Definition of a m/n Solution (c) (d)is not a real number because is not a real number.

13. Copyright © 2007 Pearson Education, Inc. Slide R-13 R.4 Review of Negative and Rational Exponents Definitions and Rules for Exponents Let r and s be rational numbers. The following results are valid for all positive numbers a and b.

14. Copyright © 2007 Pearson Education, Inc. Slide R-14 R.4 Using the Definitions and Rules for Exponents Example Evaluate each expression. (a)(b) Solution (a) (b)