1. Objective: 7.2 Properties of Rational Exponents1 Homework Answers 14. 11 1/3 38. -1/125 16. 16 5/9 40. 1/25 18. 42. 2.18 20. 44. 1.15 22. 48. -11.19 30. -10 54. -6 32. ½ 56. 0 34. -4 58. -1.41, 1.41 36. 1/81 60. 3.3066. 2.13

2. Objective: 7.2 Properties of Rational Exponents2 So Much to Learn! By the end of today, you should be able to: 1. Simplify expressions with rational exponents. 2. Use properties of rational exponents. 3. Write an expression involving rational exponents in simplest form. 4. Perform operations with rational exponents. 5. Simplify expressions that have variables and rational exponents. 6. Write an expression involving variables and rational exponents in simplest form. 7. Perform operations with rational exponents and variables.

3. Objective: 7.2 Properties of Rational Exponents3 Properties of Rational Exponents Properties of Rational Exponents: Property:Example: 1. 2. (a m ) n = a mn 3. (ab) m = a m b m 4. Notes

4. Objective: 7.2 Properties of Rational Exponents4 Properties of Rational Exponents (cont.) Properties of Rational Exponents: Property:Example: 5. 6. Notes

5. Objective: 7.2 Properties of Rational Exponents5 Using the Properties Simplify the expressions: 1. 2. 3.

6. Objective: 7.2 Properties of Rational Exponents6 More Fun with Properties 4. 5.

7. Objective: 7.2 Properties of Rational Exponents7 You Try Simplify: 1. 2. 3. 4. 5.

8. Objective: 7.2 Properties of Rational Exponents8 More Simplifying Simplify the expressions: 1. 2.

9. Objective: 7.2 Properties of Rational Exponents9 You Try Simplify: 1. 2.

10. Objective: 7.2 Properties of Rational Exponents10 Simplest Form - continued In order for a radical to be in simplest form, you have to remove any perfect n th powers and rationalize denominators. Example: Write in simplest form: 1.2.

11. Objective: 7.2 Properties of Rational Exponents11 You Try Write in simplest form:

12. Objective: 7.2 Properties of Rational Exponents12 Operations Using Radicals Two radicals expressions are “ like radicals ” if they have the same index and the same radicand. Example: Perform the indicated operation: 1.2.

13. Objective: 7.2 Properties of Rational Exponents13 You Try Perform the indicated operation:

14. Objective: 7.2 Properties of Rational Exponents14 Simplifying Expressions Involving Variables Important! = x when n is odd. = |x| when n is even.

15. Objective: 7.2 Properties of Rational Exponents15 Simplifying Simplify the expression. Assume all variables are positive: 1.2. 3. 4.

16. Objective: 7.2 Properties of Rational Exponents16 You Try Simplify the expression. Assume all variables are positive. 1. 2. 3. 4.

17. Objective: 7.2 Properties of Rational Exponents17 Writing Variable Expressions in Simplest Form Write the expression in simplest form. Assume all variables are positive. 1.2.

18. Objective: 7.2 Properties of Rational Exponents18 You Try Write the expression in simplest form. Assume all variables are positive.

19. Objective: 7.2 Properties of Rational Exponents19 Adding and Subtracting Expressions Involving Variables Perform the indicated operation. Assume all variables are positive. 1. 2. 3.

20. Objective: 7.2 Properties of Rational Exponents20 You Try Perform the indicated operations. Assume all variables are positive. 1. 2. 3.

21. Objective: 7.2 Properties of Rational Exponents21 Homework Homework: page 411, 22-30 even, 34-62 even, 66-72 even, 76, 80