Warm Up 1013 Simplify each expression 1 73

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

Notebook Table of content 19)Add, subtract, multiply polynomials 20) Dividing Polynomials 21) Factor and

8. 6 radical Expressions and Rational Exponents 1. Find all the square roots of

the nth roots of a index radicand Types of real roots Case # of

Check It Out! Example 1 5. Find all real roots. a. fourth roots of

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

Simplify the expression. Assume that all variables are positive. 8. 9. 4 10. 16

Write the expression in radical form, and simplify. 11. 64 1 3 Method 1

You try! 12. 4 Method 1. 5 2 13. Method 2 Method 1. (

Writing Expressions by Using Rational Exponents 15. 14. 13 13 4 8 1 2

You try! 16. 81 17. 3 4 18. 10 10 9 3 3 1000

Rational exponents have the same properties as integer exponents

Simplify each expression. 19. Product of Powers. 72 49 Check Enter the expression in

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

Lesson Quiz: Find all real roots. 1. fourth roots of 625 – 5, 5

Slides: 17

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Warm Up 10/13 Simplify each expression. 1. 73 • 72 8 2. 11 6 11 3. (32)3 16, 807 121 729 4. 75 5 3 5. 20 7 2 35 7

Be seated before the bell rings Agenda: DESK homework Warm-up (in your notes) Warmup Notes 8. 6

Notebook Table of content 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 1 Page 1 8. 6 Radical Expressions and Rational exponents HW ; p. 615(3 -23 odd) (35 -55 odd)

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

the nth roots of a index radicand Types of real roots Case # of roots odd 1 real root even; + radicand 2 real roots even; - radicand 0 real roots Radicand =0 1 real root examples

Check It Out! Example 1 5. Find all real roots. a. fourth roots of – 256 negative - no real fourth roots. 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.

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

Simplify the expression. Assume that all variables are positive. 8. 9. 4 10. 16 x 4 x 8 4 3 4 4 4 2 • x 3 x 9 x 3 4 24 • x 4 2 x 2 x 4 27 3 x 2

10.

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

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

Writing Expressions by Using Rational Exponents 15. 14. 13 13 4 8 1 2 n am = a Simplify. m n 15 5 13 133 2197 n a m =a m n Simplify.

You try! 16. 81 17. 3 4 18. 10 10 9 3 3 1000 5 Simplify. 5 2 4 1 2 Simplify.

Rational exponents have the same properties as integer exponents

Simplify each expression. 19. Product of Powers. 72 49 Check Enter the expression in a graphing calculator. Simplify. Evaluate the Power.

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

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