1. Splash Screen Unit 6 Exponents and Radicals

2. Splash Screen Essential Question: How do you evaluate expressions involving rational exponents?

3. Lesson Menu 5 minute check on Unit 5. Do the first 5 problems!

4. Over Lesson 7–2 5-Minute Check 1 A.49 B. C. D.

5. Over Lesson 7–2 5-Minute Check 2 A. B. 2n 4 C. D.

6. Over Lesson 7–2 5-Minute Check 3 A. B. C. D.

7. Over Lesson 7–2 5-Minute Check 4 A. B. C. D.

8. Over Lesson 7–2 5-Minute Check 6 A.B. C.D.

9. Then/Now You used the laws of exponents to find products and quotients of monomials. Evaluate and rewrite expressions involving rational exponents. Solve equations involving expressions with rational exponents. EQ: How do evaluate expressions involving rational exponents?

10. Vocabulary rational exponent radical cube root nth root exponential equation

11. What is a rational number? A rational number is any number that can be expressed as the quotient or fraction of two integers, with the denominator not equal to zero.

14. What is a RADICAL? If n is a positive integer that is greater than 1 and a is a real number then, where n is called the index, a is called the radicand, and the symbol √ is called the radical.

15. Square Root - easy definition A number that when multiplied by itself equals a given number. Root A number that, when multiplied by itself some number of times, equals a given number.

16. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 11 2 = 121 12 2 = 144 Perfect Cubes 1 3 = 1 2 3 = 8 3 3 = 27 4 3 = 64 5 3 = 125 6 3 = 216 7 3 = 343 8 3 = 512 9 3 = 729 10 3 = 1000 11 3 = 1,331 12 3 = 1,728

17. Concept Square Root

18. Example 1A Radical and Exponential Forms Answer: 9 Write each expression in radical form, or write each radical in exponential form. = 9Simplify.

19. Example 1B Radical and Exponential Forms Write each expression in radical form, or write each radical in exponential form. Answer:

20. Example 1C Radical and Exponential Forms Write each expression in radical form, or write each radical in exponential form. Answer:

21. Example 1D Radical and Exponential Forms Write each expression in radical form, or write each radical in exponential form. Answer: 9

22. Example 1CYP A.16 B.8 C.4 D.2

23. Example 1CYP Write each expression in radical form.

24. Example 1CYP Write each radical in exponential form.

25. End of the Lesson Assignment: Do Worksheet #1 to #9 Assignment: Do Worksheet #1 to #9 EQ: How do you evaluate expressions involving rational exponents?

26. Concept

27. Example 2A nth Roots A. Answer: 4

28. Example 2B nth Roots B. Answer: 5

29. Example 2A A.343 B.81 C.49 D.7

30. Example 2A Simplify.

31. Concept

32. Cube Root nth Root

33. Example 3 Evaluate b Expressions Answer: 11 A. = 11Simplify.

34. Example 3 Evaluate b Expressions Answer: 7 = 7Simplify. B.

35. Example 3 A.4 B.8 C.16 D.32

36. Example 3 Simplify.

37. End of the Lesson Assignment: Do Worksheet #10 to #18 Assignment: Do Worksheet #10 to #18 EQ: How do you evaluate expressions involving rational exponents?

38. Concept

39. Example 4A Evaluate b Expressions Answer: 4 = (2) 2 2 5 = 32 = 4Simplify.

40. Example 4B Evaluate b Expressions Answer: 59,049 = (9) 5 9 2 = 81 = 59,049Simplify.

41. Example 4 A.216 B.36 C.18 D.6

42. Example 4 Simplify.

43. End of the Lesson Assignment: Do Worksheet #19 to #21 Assignment: Do Worksheet #19 to #21 EQ: How do you evaluate expressions involving rational exponents?

44. Concept

45. Example 5A Solve Exponential Equations A. Solve 9 x = 729. 9 x = 729 Original equation 9 x = 9 3 Rewrite 729 as 9 3. x= 3 Power Property of equality

46. Example 5B Solve Exponential Equations B. Solve 16 2x – 1 = 8. 16 2x – 1 = 8 Original equation (2 4 ) 2x – 1 = 2 3 Rewrite 16 as 2 4 and 8 as 2 3. 2 8x – 4 = 2 3 Power of a Power, Distributive Property 8x – 4= 3 Power Property of Equality 8x = 7 Add 4 to each side. Divide each side by 8.

47. Example 5A Solve 9 3 x + 1 = 27 4. A. B. C. D.2

48. Example 5A Solve 6 x = 216.

49. Example 5A Solve each equation. Solve 25 x - 1 = 5.

50. End of the Lesson Assignment: Complete the Worksheet EQ: How do you evaluate expressions involving rational exponents?