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Simplifying Expressions with Rational Exponents

Learn how to write expressions in radical and exponential forms, evaluate expressions with rational exponents, solve equations, and simplify radical expressions.

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Simplifying Expressions with Rational Exponents

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 6–5) CCSS Then/Now Key Concept: Example 1: Radical and Exponential Forms Example 2: Evaluate Expressions with Rational Exponents Key Concept: Rational Exponents Example 3: Real-World Example: Solve Equations with Rational Exponents Example 4: Simplify Expressions with Rational Exponents Example 5: Simplify Radical Expressions Concept Summary: Expressions with Rational Exponents Lesson Menu

  3. A. B. C. D. 5-Minute Check 1

  4. A. B. C. D. 5-Minute Check 2

  5. A. B. C. D. 5-Minute Check 3

  6. A. B. C. D. 5-Minute Check 4

  7. A. B. C. D. 5-Minute Check 5

  8. A. B. C. D. 5-Minute Check 6

  9. Mathematical Practices 1 Make sense of problems and persevere in solving them. CCSS

  10. You used properties of exponents. • Write expressions with rational exponents in radical form and vice versa. • Simplify expressions in exponential or radical form. Then/Now

  11. Concept

  12. A. Write in radical form. Definition of Answer: Radical and Exponential Forms Example 1

  13. B. Write in exponential form. Answer: Definition of Radical and Exponential Forms Example 1

  14. A. Write in radical form. A. B. C. D. Example 1

  15. B. Write in exponential form. A. B. C. D. Example 1

  16. A.Evaluate . Answer: Evaluate Expressions with Rational Exponents Method 1 Simplify. Example 2

  17. Power of a Power Multiply exponents. Answer: Evaluate Expressions with Rational Exponents Method 2 Example 2

  18. B. Evaluate . Factor. Power of a Power Expand the square. Find the fifth root. Evaluate Expressions with Rational Exponents Method 1 Answer: 4 Example 2

  19. 32 = 25 Power of a Power Multiply exponents. 22 = 4 Evaluate Expressions with Rational Exponents Method 2 Answer: 4 Example 2

  20. A.Evaluate . A. B. C. D. Example 2

  21. B.Evaluate . A. B. C. D. Example 2

  22. Concept

  23. WEIGHTLIFTING The formulacan be used to estimate the maximum total massthat a weightlifter of mass B kilograms can liftusing the snatch and the clean and jerk. Original formula B = 168 Solve Equations with Rational Exponents According to the formula, what is the maximumthat a weightlifter weighing 168 kilograms can lift? Answer: The formula predicts that he can lift at most 472 kg. Example 3

  24. Use the formula where M isthe maximum total mass that a weightlifter ofmass B kilograms can lift. According to theformula, what is the maximum that a weightliftercan lift if he weighs 80 kilograms? A. 300 kg B. 340 kg C. 380 kg D. 400 kg Example 3

  25. A.Simplify . Multiply powers. Add exponents. Answer: Simplify Expressions with Rational Exponents Example 4

  26. B.Simplify . Multiply by . Simplify Expressions with Rational Exponents Example 4

  27. Answer: Simplify Expressions with Rational Exponents Example 4

  28. A. Simplify . A. B. C. D. Example 4

  29. B. Simplify . A. B. C. D. Example 4

  30. A.Simplify . Rational exponents 16 = 24 Power of a Power Simplify Radical Expressions Example 5

  31. Quotient of Powers Simplify. Answer: Simplify Radical Expressions Example 5

  32. B.Simplify . Rational exponents 22 = 4 Power of a Power Multiply. Simplify. Answer: Simplify Radical Expressions Example 5

  33. C. Simplify . is the conjugate of . Multiply. Answer: Simplify Radical Expressions Example 5

  34. A. Simplify . A. B. C. D. Example 5

  35. B. Simplify . A. B. C. D. Example 5

  36. C. Simplify . A. B. C. D. Example 5

  37. Concept

  38. End of the Lesson

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