By S.-V. Stratila, D.-V. Voiculescu
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Extra resources for Representations of AF-Algebras and of the Group U-infinity
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8 # 2Ϫ3 # 5 3. (Ϫ3)5 8. Ϫ32 # 5 13. 8Ϫ2 18. 5 # 2Ϫ4 # 32 4. (Ϫ4)2 9. 90 14. 3Ϫ4 19. Ϫ6 # 3Ϫ2 # 81 5. Ϫ52 10. Ϫ8x0 15. Ϫ6 # 52 20. qxd 8/7/12 26 5:34 PM Page 26 C H A P T E R 0 Prerequisites and Review In Exercises 21–50, simplify and write the resulting expression with only positive exponents. 21. x2 # x3 22. y3 # y5 23. x2 xϪ3 24. y3 # yϪ7 25. (x2 ) 26. (y3)2 27. (4a)3 28. (4x2) 29. (Ϫ2t)3 30. (Ϫ3b)4 31. (5xy2) (3x3y) 3 33. x5 y3 34. 7 xy b -4 37. a b 2 41. 2 45. 42. y5 x2 35. -2 -5 y x (2xy)2 (- 2xy) Ϫ2 y-4 x5 46.
9 ϫ 105 65. 1 ϫ 10Ϫ5 66. 0 * 10 cell phones being used worldwide. Assume that the average cell phone measures 5 inches in length and there are 5280 feet in a mile. 9 67. Cell Phones Spanning the Earth. a. If all of the cell phones currently in use were to be lined up next to each other tip to tip, how many feet would the line of cell phones span? Write the answer in scientific notation. b. The circumference of the Earth (measured at the equator) is approximately 25,000 miles. If the cell phones in part (a) were to be wrapped around the Earth at the equator, would they circle the Earth completely?
234492 10. 2549 11. 9949 12. 9951 14. 327491 15. 238473 16. qxd 16 8/7/12 5:34 PM Page 16 C H A P T E R 0 Prerequisites and Review In Exercises 17–40, perform the indicated operations in the correct order. 17. 5 ϩ 2 # 3 Ϫ 7 21. 2 Ϫ 3[4(2 # 3 ϩ 5)] 18. 2 ϩ 5 # 4 ϩ 3 # 6 22. 4 # 6(5 Ϫ 9) 19. 2 # (5 ϩ 7 # 4 Ϫ 20) 20. Ϫ3 # (2 ϩ 7) ϩ 8 # (7 Ϫ 2 # 1) 23. 8 Ϫ (Ϫ2) ϩ 7 24. Ϫ10 Ϫ (Ϫ9) 28. Ϫa ϩ b Ϫ(Ϫc) 25. Ϫ3 Ϫ (Ϫ6) 26. Ϫ5 ϩ 2 Ϫ (Ϫ3) 27. x Ϫ (Ϫy) Ϫ z 29. Ϫ(3x ϩ y) 30. Ϫ(4a Ϫ 2b) 31. 33. Ϫ4 Ϫ6 [(5 Ϫ 8)(4)] 34.