Math 2 Unit 8 Worksheet 1 Name: Properties of Exponents Date: Per: [1-] Expand and evaluate. 1. 4 2. 2 5. 4 [4-6] Rewrite each expression using only one base. You do not need to work out the final answer. 4. 2 5 5. 11 4 11 11 2 6. 5 7 5 4 5 2 [7-21] Simplify each expression. 7. (7aa 2 )(aa 4 ) 8. ( 4xxxx 2 )(15xx 4 yy 5 ) 9. 4kk(7jj 2 kk ) 10. bb 2 cc aa 2 bb 5 cc aa 4 cc 7 11. 12mm 5 (mm nn 5 ) 12. (6pp 2 qq)( 4pp 2 qq 4 ) 1. (aa 2 ) 4 14. (kk 1 ) 15. (2xx) 4 16. (5zz 5 ) 0 17. (5 2 h ) 2 18. (xx 2 y) 5 19. (7gg 4 h 0 ) 20. 4jjkk 2 (2jj 4 ) 21. ( 6aa 2 bb) 2 ( bb) Math 2 Unit 8 Worksheet 1
[22-0] Simplify each expression. Write the final answer using only positive exponents. 22. ww8 ww 2. xx8 yy 6 xx 2 yy 4 24. aa bb 7 aa 9 bb 4 25. mm nn 26. yy yy 10 xxyy7 27. xx 5 yy 28. 7xx 1 29. (2xx) 1 0. xx 2 [1-2] True or False. 1. Is (yy mm ) nn = (yy nn ) mm a true statement? Pick values for yy, mm and nn to show your answer is correct. 2. Is xx 4 xx = (xx 4 ) a true statement? Pick values for xx to show your answer is correct. Math 2 Unit 8 Worksheet 1
Math 2 Unit 8 Worksheet 2 Name: Rational Exponents Date: Per: 1. yy = 2 xx is graphed to the right. Complete the table and label points B, C, D, E, F from the table onto the graph. A xx yy = 2 xx Point A 8 Point B 2 Point C 1 Point D 1 2 Point E 0 Point F -1 [2-4] Write the expression in radical form. 2. kk 2. 2 5 4. xx 1 [5-7] Write the expression in exponential form. 5. 2xx 6. ff 2 4 7. 5xx [8-19] Evaluate the expression. 8. 16 4 9. 25 2 10. 256 4 11. 64 1 6 12. 64 5 6 1. 64 5 6 Math 2 Unit 8 Worksheet 2
14. 16 2 15. 27 2 16. ( 8) 1 17. ( 27) 2 18. (64) 1 2 19. ( 125) 4 [20-2] Simplify. Leave answer in simplified radical form when necessary. All variables represent positive numbers. 20. (25xx 2 ) 1 2 21. (8xx 4 ) 1 2 22. 2 4 2 5 4 2. 1 5 10 [20-2] Simplify. Leave answer in simplified radical form when necessary. 24. 5 1 6 5 1 4 25. 7 1 2 2 7 26. 2 9 2 5 27. xx 1 4 Math 2 Unit 8 Worksheet 2
Math 2 Unit 8 Worksheet Name: Simplify Exponential Expressions Date: Per: [1-6] Use exponents to fill in the blanks. 1. xx xx = xx 7 2. xx 4 xx = xx 12. 5 2 5 = 5 11 4. aa aa 4 = 1 5. xx 12 xx = xx 5 6. xx xx 8 = xx 2 [7-10] Find the value of x. 4 7. 15 4 15 6 = 15 xx 4 8. 25 2 25 4 = 25 xx 9. 7 4 7 6 9 = 7 xx 10. 5 4 5 2 6 = 5 xx [11-16] Simplify each expression. Write the final answer using only positive exponents. 11. (2xx) 12. 2xx 1. (mm)4 (6mm) 2 14. 6xxyy 1 2xx 2 yy 1 5 21mm4 15. 1 mm4 16. xx4 2yy 5 Math 2 Unit 8 Worksheet
17. xx 5 yy 2 21xx 8 yy 9 18. 8ww 9 xx ww 2 xx 2 19. 7aa bb 8 28aa 7 bb 12 20. nn2 (5 0 ) 4nn 21. 2mm4 mm 2 4 22. 9tt 2 4tt 2. (mm1 2) (9mm) 1 2 24. (6xx1 ) 2 (2xx 5 ) (8xx) 1 25. 75 2 7 26. 8 7 6 27. 8 4 8 6 2 4 28. 7 5 6 7 2 6 Math 2 Unit 8 Worksheet
Math 2 Unit 8 Worksheet 4 Name: Simplifying Radical Expressions Date: Per: [1-21] Express in simplest radical form. All variables represent positive numbers. 1. 20 2. 6. 50mm nn 4. 72aa 4 bb 6 5. 225kk 5 6. 5 160mm 8 7. 40dd 8 8. 500mm 9. 216aa 9 bb 7 cc 5 10. 12 0 11. 5 4 8 12. 7 48 27 1. 4xx 8xx 14. 12 21aa 2 bb 5 56aa bb 15. + Math 2 Unit 8 Worksheet 4
16. 5 + 6 5 17. 2 7 + 6 18. 12 + 48 19. 72 50 + 7 2 20. 9 + 5 4 + 7 21. 5 7 + ( 7 + 8 7) [22-0] Rationalize and simplify each expression. 22. 1 2. 2 5 24. 14 7 25. 20 15 26. 4 27. 25 6 28. 2 18 29. 14 2 5 0. 15 9 5 Math 2 Unit 8 Worksheet 4
Math 2 Unit 8 Worksheet 5 Name: Rational and Irrational Numbers Date: Per: [1-27] Simplify radical expressions, then circle R for rational answers and Ir for Irrational answers. 1. 1 4 + 2 5 R Ir 2. 2 5 + 6 5 R Ir. 5 1 7 1 R Ir 4. 4 11 + 11 R Ir 5. + 6 17 + (4 + 2 17) R Ir 6. 2 6 + 7 R Ir 7. + 7 2 ( 5 + 7 2) R Ir 8. 2 + 8 6 2 + 6 R Ir 9. 5 4 9 R Ir 10. 7 2 7 R Ir 11. 5 2 R Ir 12. 2 5 7 R Ir 1. 4 12 2 R Ir 14. 4 6 8 R Ir 15. 7 6 14 R Ir 16. 7 5 2 5 R Ir 17. 7 75 R Ir 18. 10 7 5 R Ir [19-25] Based on the work you completed in problems 1-18, make the following conjunctures. 19. What can you say about the sum of any two rational numbers? 20. What can you say about the sum of a rational and irrational number? Math 2 Unit 8 Worksheet 5
21. What can you say about the product of any two rational numbers? 22. What can you say about the product of a rational and irrational number? 2. Can the sum of two irrational numbers be rational? Give an example: 24. Can the product of two irrational numbers be rational? Give an example: 25. From the numbers: 5, 6, 2 6, 2 6, 5, 6, choose two numbers that when you: a. multiply them, it is rational, AND when you add the same two numbers, it is irrational. b. multiply them, it is irrational, AND when you add the same two numbers, it is irrational. [26-29] Simplify and determine whether each expression is equivalent to 8xx 5 4. Check the appropriate box. Yes No 26. 16 4 xx 5 4 27. 16xx 5 4 4 28. 8 xx 5 4 29. 8xx 5 Math 2 Unit 8 Worksheet 5
Math 2 Unit 8 Review Worksheet Name: No Calculators Allowed Date: Per: [1-4] Simplify each expression. 1. 7 + 2 + (8 ) 2. + 2 1 (2 4 1). 10 + 5 7 ( 4 2 7) 4. 5 + 2 5 ( 7 5) 5. Complete the table. Simplify each expression and check the appropriate box for Rational or Irrational numbers. 2 + 5 (2 2) Simplified Expression Rational Irrational 17 5 + 5 100 + 4 16 14 7 4 6. Provide a counter example for the following statements: a. The sum of 2 irrational square root numbers is Always irrational. b. The product of 2 irrational square root numbers is Always irrational. c. The sum of 2 irrational cube root numbers is Always irrational. d. The product of 2 irrational cube root numbers is Always irrational. Math 2 Unit 8 Review Worksheet
7. From the numbers:, 5,, 5, 5, 5, choose two numbers that when you: a. multiply them, it is rational, AND when you add the same two numbers, it is irrational. b. multiply them, it is irrational, AND when you add the same two numbers, it is irrational. [8-1] Simplify each expression. Write the final answer using only positive exponents. 8. (2xx 2 yy 7 ) 9. ( 4xx 4 yy 2 ) 2 10. xx4 yy 2 2 11. (xx kk 4 )(xx 2 kk ) 4 12. mm 2 kk (mm 2 kk 4 ) 1. xx 4 yy(xx yy 2 ) 2 14. (7xx 2 yy 5 )(xx 10 )( 2yy 10 ) 2 15. 5xx 5 yy 2 (2xx 14 ) 2 16. zz(yy 5 zz 7 ) 1 yy 5 17. xx 5 yy 4 xx yy 18. aa 5 bb aa 2 bb 5 19. xx 7 rr 4 xx 2 rr 20. 4mm 2 nn 5 pp 2mm 7 nn pp 8 21. 21xx 7 yy 2 zz 4 7xx 5 yy 8 zz 9 22. 20ss tt 2 vv 5ss 2 tt vv 2. (xx 2 ) 24. (2xx 1 ) 6 25. (4xx 1 5) 2 Math 2 Unit 8 Review Worksheet
26. 64 4/ 27. 25 /2 28. 125 1/ 29. xx5 xx 2 10 0. 5 xx2 xx 2 4 1. 4 xx5 10 xx 4 [2-4] Write in exponential form. 5 2. xx 4. xx 2 4 4 4. xx 6 8 [5-7] Simplify and write in exponential form. 5. 2 2 9 2 2 6. 5 6 7. 6 4 5 6 [8-40] Complete the table. Write in simplified exponential and radical form. Expression Simplified Exponent Form Simplified Radical Form 8. (27xx) 2 9. (81xx ) 4 40. (16xx 5 ) 2 [41-4] Simplify and express answer in radical form. 41. 8 1 6 8 1 4 42. dd 2 dd 5 4. 2 1 5 2 1 Math 2 Unit 8 Review Worksheet
[44-49] Write in exponential form, then solve for x. 44. 16 16 10 = 16 xx 2 45. 64 7 64 7 = 64 xx 46. 82 8 4 6 = 8 xx 6 47. 74 7 2 5 = 7 xx 20 6 1 48. 4 = 1 xx 49. 2 1 2 = 2 1 xx 50. Complete the table. Write an Equivalent Expression to the following in the form of aa mm aa nn and (aa nn ) mm aa mm aa nn (aa nn ) mm aa 14 xx 12 pp 20 Math 2 Unit 8 Review Worksheet