1. Lesson Menu

2. Over Lesson 7–2 5-Minute Check 1

3. Splash Screen Rational Exponents Lesson 7-3

4. Then/Now Understand how to rewrite and evaluate expressions involving rational exponents and solve equations containing rational expressions.

5. Vocabulary

6. Concept

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

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

9. Example 1CYP

10. Concept

11. Example 2A nth Roots A. B. C.

12. Concept

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

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

15. Example 3

16. Concept

17. Example 4A Evaluate b Expressions Answer: 4 = 2 2 2 5 = 32 = 4Simplify.

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

19. Example 4

20. Concept

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

22. 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= 3Power Property of Equality 8x = 7Add 4 to each side. Divide each side by 8. Answer:

23. Example 5A Solve 93 x + 1 = 27 4.

24. Example 6 BIOLOGY The population p of a culture that begins with 40 bacteria and doubles every 8 hours can be modeled by, where t is time in hours. Find t if p = 20,480. Original equation p = 20,480 Divide each side by 40. Solve Exponential Equations

25. Example 6 Solve Exponential Equations Rewrite 512 as 2 9. 72= tMultiply each side by 8. Power Property of Equality Answer:72

26. Example 6 NEWS The number of hits to a news story online can be modeled by, where t is time in hours. Find t if h = 24,576.

27. End of the Lesson Homework p