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Chapter 5 Section 7 Rational Exponents

Chapter 5 Section 7 Rational Exponents. Objectives: To write expressions with rational exponents in radical form and vice versa. To simplify expressions in exponential or radical form. Warm-up: Type 1 writing. 3 lines or more – 2 minutes

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Chapter 5 Section 7 Rational Exponents

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  1. Chapter 5 Section 7Rational Exponents Objectives: To write expressions with rational exponents in radical form and vice versa. To simplify expressions in exponential or radical form

  2. Warm-up: Type 1 writing 3 lines or more – 2 minutes Write two expressions with radicals, one that is simplified and one that is not. Explain the difference between the two.” 30 seconds Finish your thought.

  3. Warm-up: Type 1 writing 3 lines or more – 2 minutes Write two expressions with radicals, one that is simplified and one that is not. Explain the difference between the two.” Times up! Put your pencils down.

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

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

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

  7. Write each expression in radical form. a. b. Answer: Answer: Example 7-1c

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

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

  10. Write each radical using rational exponents. a. b. Answer: Answer: Example 7-2c

  11. Evaluate Method 1 Answer: Simplify. Example 7-3a

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

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

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

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

  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. 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.

  17. 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.

  18. 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.

  19. Practice – Adding/Multiplying Fractions

  20. Simplifying Rational Exponents • Has no negative exponents • Has no fractional exponents in the denominator • Is not a complex fraction • The index is the smallest number possible

  21. Simplify . Multiply powers. Answer: Add exponents. Example 7-5a

  22. Simplify . Multiply by Example 7-5b

  23. Answer: Example 7-5c

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

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

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

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

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

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

  30. End of Lesson 7

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