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

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5-Minute Check 1

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5-Minute Check 1

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

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5-Minute Check 2

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5-Minute Check 3

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5-Minute Check 3

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

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

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5-Minute Check 5

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5-Minute Check 5

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5-Minute Check 6

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5-Minute Check 6

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

16. 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

17. Concept

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

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

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

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

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

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

24. B. Write in exponential form.C. D.
Example 1

25. B. Write in exponential form.C. D.
Example 1

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

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

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

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

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

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

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

33. 32 = 25 Method 2 Power of a Power Multiply exponents. 22 = 4 Answer: 4
Evaluate Expressions with Rational Exponents
32 = 25
Method 2
Power of a Power
Multiply exponents.
22 = 4
Answer: 4
Example 2

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

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

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

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

38. Concept

39. Solve Equations with Rational Exponents
WEIGHTLIFTING The formula can be used to estimate the maximum total mass that a weightlifter of mass B kilograms can lift using the snatch and the clean and jerk.
According to the formula, what is the maximum that a weightlifter weighing 168 kilograms can lift?
Original formula
B = 168
Answer:
Example 3

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

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

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

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

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

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

46. Simplify Expressions with Rational Exponents
Answer:
Example 4

47. Simplify Expressions with Rational Exponents
Answer:
Example 4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

65. Concept

66. End of the Lesson