Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
NAME DATE 7-3 PERIOD Study Guide and Intervention Rational Exponents Rational Exponents For any real numbers a and b and any positive integer n, if an = b, then a is an nth root of b. Rational exponents can be used to represent nth roots. ! Square Root 𝑏! = 𝑏 Example 1 ! (6𝑥𝑦)! = ! Cube Root 𝑏! = nth Root 𝑏! = ! 𝟏 ! 𝑏 𝑏 𝟏 Example 2 Write (𝟔𝒙𝒚)𝟐 in radical form. 6𝑥𝑦 ! ! ! 625! = Definition of 𝑏 ! ! Simplify 𝟔𝟐𝟓𝟒 . ! 𝑏! = 625 ! ! 𝑏 625 = 5 = 5∙5∙5∙5 =5 4 Simplify. Exercises Write each expression in radical form, or write each radical in exponential form. ! ! ! 2. 5𝑥 ! 3. 17𝑦 ! ! 4. 12! 5. 19𝑎𝑏 ! 6. 17 7. 12𝑛 8. 18𝑏 9. 37 Lesson 7-3 ! 1. 14! Simplify. 10. ! 343 11. ! 1024 13. ! 2401 14. ! 64 16. ! 1331 17. ! Chapter 7 ! 12. 512! ! 15. 243! ! 6561 18. 4096! 17 Glencoe Algebra 1 NAME DATE 7-3 PERIOD Study Guide and Intervention (continued) Rational Exponents Solve Exponential Equations In an exponential equation, variables occur as exponents. Use the Power Property of Equality and the other properties of exponents to solve exponential equations. Example Solve 1024x − 1 = 4. 1024x − 1 = 4 (45)x − 1 = 4 45x − 5 = 41 5x − 5 = 1 5x = 6 ! x= ! Original equation 5 Rewrite 1024 as 4 . Power of a Power, Distributive Property Power Property of Equality Add 5 to each side. Divide each side by 5. Exercises Solve each equation. 1. 2x = 128 2. 33x + 1 = 81 3. 4x – 3 = 32 4. 5x = 15,625 5. 63x + 2 = 216 6. 45x – 3 = 16 7. 8x = 4096 8. 93x + 3 = 6561 9. 11x – 1 = 1331 10. 3x = 6561 11. 25x + 4 = 512 12. 7x – 2 = 343 13. 8x = 262,144 14. 55x = 3125 15. 92x – 6 = 6561 16. 7x = 2401 17. 73x = 117,649 18. 62x – 7 = 7776 19. 9x = 729 20. 83x + 1 = 4096 21. 133x – 8 = 28,561 Chapter 7 18 Glencoe Algebra 1