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Name Date Exponents and Polynomials Write the letter of the correct answer. 1. Simplify (x6)3. C A x9 C x18 B x3 D x2 2. Simplify [(a b)3]2. D 3 A (a b) 2 C (a b)1 B (a b)5 D (a b)6 45 4 3. Find the quotient of 4 . A A 4 C 1 1 B 1 4 D 64 4. Find the quotient of (4x 2y)5 (4x 2y)7, 4x 2y 0. C A (4x 2y)2 C (4x 2y)2 B (4x D (4x 2y) 2y)12 5 7 5. What is 4,000,000,000 in scientific notation? B A 4.0 • 108 C 409 B 4.0 • 109 D 4.0 • 1010 6. What is 3.14(104) in standard notation? B A 31,400 C 0.00314 B 0.000314 D 3.000014 © 2004 by CompassLearning, Inc. © by AGS Publishing. Permission is granted to reproduce for classroom use only. Chapter 5 Review Name Date Exponents and Polynomials (continued) Find the sum, difference, product, or quotient. Write your answer in scientific notation. Example: 2(103) 2(103) Solution: 2(103) 2(103) 4(103) 7. 3.1(10–4) 4.2(10–4) 7.3(10–4) 8. 4.7(10–2) 3.6(10–2) 1.1(10–2) 9. 1.3(10–6) • 4.2(10–4) • 1.9(102) 1.0374(10–7) 10. 8.58(10–4) 4.29(10–4) 2.0 11. 0.2825(10–6) 1.13(102) 2.5(10–9) Find the sum and the difference for each pair of polynomials. Example: Subtract x2 2y 2 x2 y 1 Solution: Add x2 2y 2 2 y 1 x 2x2 y 3 x2 2y 2 x2 2y 2 – (x2 y 1) (1)(x2 y 1) x2 2y 2 2 x y 1 3y 1 12. 3y 5 2y 3 1y 3 15. m5 m3 5 4y 5 5y 3 7y 8 m4 m2 5 13. 2x 4 4x 3 6x 2 8x 10 3x 4 5x 3 7 16. 4x 4 + 8x3 + 16x 2 + 4 4x 3 + 2x 2 + 16x 14. b4 4b3 6b2 4b 1 3b4 3b3 5b2 4b 12. 7y 5 7y 3 6y 5; y 5 3y 3 8y 11 13. 5x 4 x 3 6x 2 8x 17; x 4 9x 3 6x 2 8x 3 14. 2b 4 b 3 11b 2 1; 4b 4 7b 3 b 2 8b 1 15. m 5 m 4 m 3 m 2; m 5 m 4 m 3 m 2 10 16. 4x 4 12x 3 18x 2 16x 4; 4x 4 4x 3 14x 2 16x 4 © 2004 by CompassLearning, Inc. © by AGS Publishing. Permission is granted to reproduce for classroom use only. Chapter 5 Review Name Date Exponents and Polynomials (continued) 17. 18x 4 2x 3 14x 2 Find the product. Example: (x 2)(x 2) Solution: (x 2)(x 2) = x(x 2) 2(x 2) x2 4x 4 17. 2x 2(9x 2 x 7) 21. (4x 3)(x 2) 18. (x 3)(9x 4) 22. (m3 m2)2 19. (4y 2 + 4)(–3y – 3) 23. (m4 5)(2m3 3m2 2) 20. (x + 5)(x + 4) 10x2 20x 5 19. 12y 3 12y 2 12y 12 20. x 2 9x 20 21. 4x 2 5x 6 22. m 6 2m 5 m 4 Find the quotients. Identify any remainder. Use multiplication to check your answer. Example: 5 18. 9x 5 27x 4 2 10x + 20x + 5 Solution: 5 2x2 4x 1 (12y3 18y 36) 6 (30x3 25x2 20x 10) 25. 5 (p2 2p)2 26. (p2 2p) (3x2 6x) 27. x(x 2) 24. 23. 2m 7 3m 6 2m 4 10m 3 15m 2 10 2y 3 3y 6 6x 3 5x 2 4x 2 p 2 2p 3 2 28. (33x3 24x 2 18x 12) 3x 11x 8x 6 r–12 29. (x3 49x) (x 7) (x 2 7x) or x(x 7) 30. (5x – 1)15 x3 3x 12 8x 1 4 3x 2 – 2x – 4 Test-Taking Tip: When you study for chapter tests, practice the step-by-step formulas and procedures. © 2004 by CompassLearning, Inc. © by AGS Publishing. Permission is granted to reproduce for classroom use only. Chapter 5 Review