1. Warm Up 10/13 Simplify each expression. 16,807 121 729 1. 7 3 7 2 3. (3 2 ) 3 2. 11 8 11 6 4. 5. 75 20 7 2 35 7 5 3

2. Be seated before the bell rings DESK homework Warm-up (in your notes) Agenda: Warmup Notes 8.6

3. Notebook Table of content Page 1 1 19)Add, subtract, multiply polynomials 20) Dividing Polynomials 21) Factor and find roots 22) Fundamental Theorem of Algebra 23)Graph of polynomials 24) Radical Expressions and Rational exponents 8.6 Radical Expressions and Rational exponents HW ; p.615(3-23 odd) (35-55 odd)

4. 8.6 radical Expressions and Rational Exponents 1. Find all the square roots of 25 2. Find all the fifth roots of 32 3. Find all the cube roots of -64 4. Find all the fourth roots of -625

5. the nth roots of a Types of real roots Case# of rootsexamples index odd1 real root even; + radicand radicand 2 real roots even; - radicand 0 real roots Radicand =0 1 real root

6. 5. Find all real roots. a. fourth roots of –256 negative - no real fourth roots. Check It Out! Example 1 b. sixth roots of 1 positive - two real sixth roots. X = 1 and –1. c. cube roots of 125 positive - one real cube root. X= 5.

7. 3  x  x  x 3x33x3 Simplifying Radical Expressions 6. 7.

8. Simplify the expression. Assume that all variables are positive. 2  x 2x2x 44 16x 4 2 4 4 x 4 4 2 4x 4 8.9. 8 4 4 3 x 4 2 27 3 x 10. x3x3 3 9 x

10. Method 1 Evaluate the root first. (4) 1 64 1 3 4 Write the expression in radical form, and simplify. Method 2 4  1 3 64  1 3 3 11.

11. Method 1. (2) 5 4 5 2 32 You try! 12. Method 2 32  5 2 4  5 2 4 2 1024 625 3 4 13. (5) 3 125  3 4 625 125  3 4 625 4 244,140,625 Method 1.Method 2

12. Writing Expressions by Using Rational Exponents Simplify. 15 5 13 1 2 Simplify. 14. 15. 4 8 13 13 3 2197  m m n n a  m m n n

13. Simplify. 16.17. 3 4 81 10 3 You try! 9 3 10 1000 Simplify. 5 1 2 18. 2 4 5

14. Rational exponents have the same properties as integer exponents

15. Product of Powers. Simplify each expression. 19. Simplify. Evaluate the Power. 7272 49 Check Enter the expression in a graphing calculator.

16. Simplify each expression. 1 4 6 20. 21. (–8) – 1 3 22. 1 –8 1 3 1 2 –

17. Lesson Quiz: Find all real roots. –5, 5 1. fourth roots of 625 2. fifth roots of –243 –3 Simplify each expression. 2 4. 4y24y2 5. Write (–216) in radical form and simplify. 2 3 6. Write using rational exponents. 5 3 21 3. 8 4 256y = 36   2 3 216 3 5 21