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Mastering Rational Exponents: Lessons and Exercises for Algebra II

Dive into Chapter 5.7 of Algebra II focused on rational exponents, essential for advanced algebra understanding. This comprehensive guide covers warm-up exercises, guided simplification techniques, and various examples exploring both radical and exponential forms. Each section enables students to practice and grasp the concepts, including multiplying exponents and simplifying expressions. This agenda includes detailed explanations, example problems, and evaluation methods to solidify learning. An ideal resource for both standard and honors courses.

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Mastering Rational Exponents: Lessons and Exercises for Algebra II

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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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