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Algebra II Mr. Gilbert

Algebra II Mr. Gilbert. Chapter 5.7: Rational Exponents Standard & Honors. Agenda. Warm-up (next slide) Check your answers Lesson 9.2 Questions and comments. Warm-up 5.7 (3 min.). Use a calculator if you want simplify these expressions: (x 2 )(x 3 ) (6 2 )(6 3 ) (x 2 ) 3 (4 2 ) 3

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Algebra II Mr. Gilbert

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  1. Algebra IIMr. Gilbert Chapter 5.7: Rational Exponents Standard & Honors

  2. Agenda • Warm-up (next slide) • Check your answers • Lesson 9.2 • Questions and comments

  3. Warm-up 5.7 (3 min.) Use a calculator if you want • simplify these expressions: • (x2)(x3) • (62)(63) • (x2)3 • (42)3 • (-5x2y3)2 • 52/56

  4. Warm-up 5.7 (3 min.) Use a calculator if you want • simplify these expressions: • (x2)(x3) = x5 • (62)(63) = 65 • (x2)3 = x6 • (42)3 =46 • (-5x2y3)2 = 25x4y3 • 52/56 = 1/54

  5. Gravity: Newton and the Pirates

  6. Lesson 7 Contents 5-7 Rational Exponents Example 1Radical Form (1) Example 2Exponential Form (2) Example 3Evaluate Expressions with Rational Exponents (5) Example 4Rational Exponent with Numerator Other Than 1 (3) Example 5Simplify Expressions with Rational Exponents (2) Example 6Simplify Radical Expressions (5)

  7. Write in radical form. Definition of Answer: Example 7-1b Example 1 Definition

  8. Write using rational exponents. Answer: Definition of Example 7-2a Example 2 Definition

  9. Write using rational exponents. Answer: Definition of Example 7-2b

  10. Evaluate Method 1 Answer: Simplify. Example 7-3a ! Technique

  11. Method 2 Power of a Power Multiply exponents. Answer: Example 7-3b !

  12. Evaluate . Method 1 Factor. Power of a Power Expand the square. Find the fifth root. Example 7-3c Answer: The root is 4.

  13. Method 2 Power of a Power Multiply exponents. Example 7-3d Answer: The root is 4.

  14. Evaluate each expression. a. b. Answer: Example 7-3e Answer: 8

  15. Weight LiftingThe formula can be used toestimatethe maximum total mass that a weight lifter of mass B kilograms can lift in two lifts, the snatch and theclean and jerk, combined. Original formula Use a calculator. Example 7-4a According to theformula, what is the maximum that U.S. WeightlifterOscar Chaplin III can lift if he weighs 77 kilograms? Answer:The formula predicts that he can lift at most 372 kg.

  16. Weight LiftingThe formula can be used toestimatethe maximum total mass that a weight lifter of mass B kilograms can lift in two lifts, the snatch and theclean and jerk, combined. Example 7-4b Oscar Chaplin’s total in the 2000 Olympics was 355 kg. Compare this to the value predicted by the formula. Answer:The formula prediction is somewhat higher than his actual total.

  17. Weight LiftingUse the formula where M is the maximum total mass that a weight lifter of mass B kilograms canlift. a. According to the formula, what is the maximum that a weight lifter can lift if he weighs 80 kilograms? b. If he actually lifted 379 kg, compare this to the value predicted by the formula. Example 7-4c Answer:380 kg Answer:The formula prediction is slightly higher than his actual total.

  18. Simplify . Answer: Multiply by Example 7-5b

  19. Simplify each expression. a. b. Answer: Answer: Example 7-5d

  20. Simplify . Rational exponents Power of a Power Example 7-6a

  21. Quotient of Powers Answer: Simplify. Example 7-6b

  22. Simplify . Rational exponents Power of a Power Multiply. Answer: Simplify. Example 7-6c

  23. Simplify . is the conjugate of Answer: Multiply. Example 7-6d

  24. Simplify each expression. a. b. c. Answer: Answer: Example 7-6e Answer: 1

  25. Homework Review

  26. Homework See Syllabus 5.7 pp. 261-262: 6,7, 21 - 63 multiples of 3

  27. Homework - Honors See Syllabus 5.7 pp. 261-262: 21 - 66 (multiples of 3), 67-70

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