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Warm Up 10/13 Simplify each expression.

11 8. 2. 11 6. 75. 5 3. 2 35. 20. 7. 7. Warm Up 10/13 Simplify each expression. 16,807. 1. 7 3 • 7 2. 121. 729. 3. (3 2 ) 3. 4. 5. Be seated before the bell rings. Agenda: Warmup Notes 8.6. DESK. Warm-up (in your notes). homework. Notebook. 1. Table of content.

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Warm Up 10/13 Simplify each expression.

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  1. 118 2. 116 75 5 3 2 35 20 7 7 Warm Up 10/13 Simplify each expression. 16,807 1. 73•72 121 729 3. (32)3 4. 5.

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

  3. Notebook 1 Table of content 8.6 Radical Expressions and Rational exponents Page 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 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. index the nth roots of a radicand Types of real roots Case # of roots examples odd 1 real root 2 real roots even; + radicand 0 real roots even; - radicand 1 real root Radicand =0

  6. 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.

  7. Simplifying Radical Expressions 7. 6. 3  x x x 3x3

  8. 8 4 x 4 3 3 9 x 424 •4 x4 424 •x4 27 4 2 x 3 Simplify the expression. Assume that all variables are positive. 8. 9. 10. 4 4 16 x x3 2  x 2x

  9. 10.

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

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

  12. 15 4 1 8 5 2 14. 15. 13 m m = = m m n n a a a a n n 13 13 Writing Expressions by Using Rational Exponents 133 Simplify. Simplify. 2197

  13. 2 3 1 9 3 2 4 4 5 10 81 5 You try! 16. 17. 18. 103 Simplify. Simplify. 1000

  14. Rational exponents have the same properties as integer exponents

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

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

  17. 2 3 5. Write (–216) in radical form and simplify. ( ) 2 - = 36 3 216 5 3 5 21 21 3 Lesson Quiz: Find all real roots. –5, 5 1. fourth roots of 625 –3 2. fifth roots of –243 Simplify each expression. 2 4. 4y2 8 3. 256 y 4 6. Write using rational exponents.

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