1. 7.2 Properties of Rational Exponents 3/4/2013

3. Example 1 Use Properties of Rational Exponents a. 6 2/3 6 1/3 = 6 (2/3 + 1/3) = 6 3/3 = 6161 = 6 b. (3 3/4 ) 4 = 3 (3/4 4) =3 = 27 c. (16 25) 1/2 = 20 = 16 1/2 25 1/2 = 4 5 d. 8 1/3 – 1 = = 2 1 e. 7 1/2 7 5/2 = 7 (5/2 1/2) – = 7 4/2 = 7272 = 49

4. Fourth Root Perfect Fourth 1 = 1 4 16 = 2 4 81 = 3 4 256 = 4 4 625 = 5 4

5. Fifth Root Perfect Fifth 1 = 1 5 32 = 2 5 243 = 3 5 1024 = 4 5 3125 = 5 5

6. Simplifying =5 =2 =5 =3 In general

8. Example 2 Use Properties of Radicals a. 3 3 9 3 = 3 Simplify. = 4 3 48 Quotient property of radicals = 2 Simplify. = 3 3 9 Product property of radicals = 3 3 3 Factor. 3 b. 4 48 3 4 = 2 4 2 Divide and factor. 2 2

9. Example 3 Write Radicals in Simplest Form a. 3 40 = 8 3 5 Factor out a perfect cube. = Separate the product 8 3 5 3 = 2 Simplify. 5 3 b. Factor out a perfect fifth.

10. Checkpoint Simplify the expression. Use Properties of Radicals and Rational Exponents ANSWER 2 2 3 3 1. 2 3 4 3 2. 4 5 8 5 3. 54 3 2 3 4. 81 3 3 3

11. Example 5 Simplify Expressions with Variables a. 9x 69x 6 Simplify the expression. Write your answer using positive exponents only. Assume all variables are positive. = 3x 33x 3 Simplify. b. 4y 64y 6 () 1/2 = 4 1/2 y 6 () 1/2 Power of a product property = Power of a power property = 2y 32y 3 Simplify.

12. Example 5 Simplify Expressions with Variables c. 3 y 6y 6 x 3x 3 = x y 2y 2 Simplify. d. ac 2 3a 3/2 c – Quotient of powers property 3a (3/2 1) c [1 ( 2)] = ––– Simplify. 3a 1/2 c 3 = Factor out perfect cube factors.

13. Example 5

14. Checkpoint Simplify the expression. Write your answer using positive exponents only. Assume all variables are positive. ANSWER 5y 2 ANSWER 2uv 3 1. 25y 4 ANSWER 2x 2/3 z 3 Simplify Expressions with Variables 2. y 2y 2 x 6x 6 ANSWER y x 3x 3 3. 8u 3 v 9 () 1/3 4. 2x2x x 1/3 z 3 –

15. Homework: Prac A WS 7.2 #