Warm–up #3 1. Simplify 3 −8 𝑦 0 𝑥 6 −2 2. Simplify 𝑦 4 𝑤 6

Warm–up #3 Solutions 1. Simplify 3 −8 𝑦 0 𝑥 6 −2 = 3 𝑥 6 −8 𝑦 0 2 = 3 𝑥 12 64 = 𝑥 4 4

Warm–up #3 Solutions 2. Simplify 𝑦 4 𝑤 6 = 𝑦 4 𝑤 6 = 𝑦 2 𝑤 3

Homework Log Mon 9/21 Lesson 1 – 7 Learning Objective: To understand radical & exponential forms Hw: #111 Pg. 66 #43 – 93 odd

9/21/15 Lesson 1 – 7 Rational Exponents Day 2 Advanced Math/Trig

Learning Objective To write radicals in exponential form To write exponents into radical form

Rational Exponents Rational #: ratio of 2 integers (fraction) Define: Flower Power Roots (sun) (roots)

Change into radical form 1. 𝑥 5 7 = 7 𝑥 5 2. b 𝑥 4 5 = b 5 𝑥 4

Change into radical form 3. 𝑦 2 𝑥 8 2 9 = 9 𝑦 2 𝑥 8 2 4. (5 𝑥 3 ) 1 5 = 5 5𝑥 3

Change into exponential form 5. 3 𝑥 8 = 𝑥 8 3 6. 5 𝑥 10 = 𝑥 10 5 = 𝑥 2

Change into exponential form 7. 4 𝑎𝑏 𝑐 2 3 = 𝑎𝑏 𝑐 2 3 4 8. 5 𝑎𝑦 3 = (𝑎 𝑦 3 ) 1 5 or = 𝑎 1 5 𝑦 3 5

Evaluate 9. 16 1 4 = 4 16 = 4 2 4 = 2 10. −27 8 2 3 = 3 −27 8 2 Easier to do root before power = −3 2 2 = 9 4

Evaluate 11. 16 − 3 2 = 16 −3 = 4 −3 = 1 4 3 = 1 64 12. 1 25 − 3 2 = 25 3 2 = 25 3 = 5 3 = 125

Simplify 13. ( 𝑥 1 4 𝑦 1 5 ) 20 = 𝑥 5 𝑦 4 14. 𝑥 1 2 𝑥 3 4 𝑥 1 3 Laws of Exponents! = 𝑥 5 4 𝑥 1 3 = 𝑥 11 12

Simplify 15. ( 𝑥 − 1 3 𝑦 2 3 ) − 3 2 = ( 𝑥 − 1 3 ) − 3 2 ( 𝑦 2 3 ) − 3 2 = 𝑥 1 2 𝑦 −1 = 𝑥 1 2 𝑦 16. 𝑥 1 5 ( 𝑥 4 5 − 𝑥 − 1 5 ) = 𝑥 1 5 ( 𝑥 4 5 )−( 𝑥 1 5 )( 𝑥 − 1 5 ) = 𝑥 1 5 + 4 5 − 𝑥 1 5 +(− 1 5 ) = 𝑥− 𝑥 0 = 𝑥 −1

Ticket Out the Door Simplify using laws of exponents ( 𝑥 − 3 2 + 𝑦 − 3 2 ) ( 𝑥 − 3 2 − 𝑦 − 3 2 ) Explain what you did and discuss which laws you used

Homework #111 Pg. 66 43 – 93 odd