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2(x ϩ 3) Answer: a. 2x ϩ 6 b. 5y Ϫ 15 b. 5(y Ϫ 3) You also probably know the rules that apply when multiplying a negative real number. ” P R O P E RTI E S O F N E GATIVE S MATH (LET a DESCRIPTION AND b BE POSITIVE REAL NUMBERS) EXAMPLE A negative quantity times a positive quantity is a negative quantity. (Ϫa)(b) ϭ Ϫab (Ϫ8)(3) ϭ Ϫ24 A negative quantity divided by a positive quantity is a negative quantity. or A positive quantity divided by a negative quantity is a negative quantity. -a a = b b a a = -b b - 16 = -4 4 15 = -5 -3 A negative quantity times a negative quantity is a positive quantity.
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? If so, approximately how many times? 68. Cell Phones Reaching the Moon. a. If all of the cell phones currently in use were to be lined up next to each other tip to tip, how many miles would the line of cell phones span? Write the answer in scientiﬁc notation. b. The Moon traces an elliptical path around the Earth, with the average distance between them being approximately 239,000 miles.
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.