1. Section Concepts 2.4 Definitions of b 0 and b –n Slide 1 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Definition of b 0 2.Definition of b –n 3.Properties of Integer Exponents: A Summary

2. Section Concepts 2.4 Definitions of b 0 and b –n Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Any Homework Questions ?

3. Section 2.4 Definitions of b 0 and b –n 1.Definition of Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Consider the following pattern. As the exponents decrease by 1, the resulting expressions are divided by 3. For the pattern to continue, we define

4. DEFINITION Let b be a nonzero real number. Then, b 0 = 1. Definition of b 0 Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

5. Example 1Simplifying Expressions with a Zero Exponent Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify (assume a. d. b. e. c. f.

6. Section 2.4 Definitions of b 0 and b –n 1.Definition of b 0 Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Therefore,must be defined as 1.

7. Section 2.4 Definitions of b 0 and b –n 2.Definition of b –n Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Consider the following pattern. As the exponents decrease by 1, the resulting expressions are divided by 3. For the pattern to continue, we define

8. Section 2.4 Definitions of b 0 and b –n 2.Definition of b –n Slide 8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. For the pattern to continue, we define

9. DEFINITION Let n be an integer and b be a nonzero real number. Then, Definition of b –n Slide 9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

10. Section The definition of implies that to evaluate take the reciprocal of the base and change the sign of the exponent. 2.4 Definitions of b 0 and b –n 2.Definition of b –n Slide 10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

11. Example 2Simplifying Expressions with Negative Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify. Assume that a. b. c.

12. Example 3Simplifying Expressions with Negative Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify. Assume that a.b.c.

13. Example 4Simplifying Expressions with Negative Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify. Assume that a.b. c.

14. Section 2.4 Definitions of b 0 and b –n 3.Properties of Integer Exponents: A Summary Slide 14 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Properties of Integer Exponents Assume that a and b are real numbers and that m and n represent integers.

15. Section 2.4 Definitions of b 0 and b –n 3.Properties of Integer Exponents: A Summary (continued) Slide 15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

16. Section 2.4 Definitions of b 0 and b –n 3.Properties of Integer Exponents: A Summary (continued) Slide 16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

17. Section 2.4 Definitions of b 0 and b –n 3.Properties of Integer Exponents: A Summary Slide 17 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

18. Example 5Simplifying Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify the expressions. Write the answers with positive exponents only. Assume all variables are nonzero. a.b.c.

19. Example 6Simplifying Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify the expressions. Write the answers with positive exponents only. Assume that all variables are nonzero. a.b.

20. Example 7Simplifying Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify the expressions. Write the answers with positive exponents only. Assume that all variables are nonzero. a.b.

21. Example 8Simplifying Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify the expressions. Write the answers with positive exponents only. Assume that all variables are nonzero. a.b.

22. Example 9Simplifying an Expression with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify the expression Write the answer with positive exponents only.

23. Example 2.3 Definitions of b 0 and b –n Slide 23 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Definition of b 0 2.Definition of b –n 3.Properties of Integer Exponents: A Summary

24. Example You Try: 1. Simplify each expression. Write the answers with positive exponents only. Assume all variables are nonzero. A.B.

25. Example You Try: 1. Simplify each expression. Write the answers with positive exponents only. Assume all variables are nonzero. A.B.