By Raymond Barnett, Michael Ziegler, Karl Byleen

The Barnett, Ziegler, Byleen "College Algebra" sequence is designed to be consumer pleasant and to maximise pupil comprehension. The objective of this sequence is to stress computational abilities, principles, and challenge fixing instead of mathematical idea. the massive variety of pedagogical units hired during this textual content will consultant a pupil during the direction. built-in through the textual content, the scholars and teachers will locate Explore-Discuss packing containers which motivate scholars to imagine severely approximately mathematically thoughts. In every one part, the labored examples are by way of matched difficulties that toughen the idea that being taught. additionally, the textual content comprises an abundance of workouts and purposes that might persuade scholars that math comes in handy.

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**Extra resources for College Algebra (8th edition)**

**Example text**

X 2 3xy 50. 5 2 32u12v8 uv 4 2 32m7n9 2mn 3 48. 2a2 8a8b13 49. 3 4 9 3 ab 51. 2 1 52. 21 x8 y6 6 bar67388_chR_014-035 11/2/06 17:10 Page 35 S E C T I O N R–3 3 3 53. 2 2x2y4 2 3x5y 4 4 54. 2 4m5n2 6m3n4 81. In Problems 55–60, rationalize denominators and write in simplified form. 55. 58. 12m15 120m 56. 5 1x 3 Ϫ 21x 59. 1618c 118c 57. 2 15 ϩ 3 12 5 15 ϩ 2 12 60. 31y 21y Ϫ 3 3 12 Ϫ 213 313 Ϫ 212 1 1x Ϫ 1y ϩ 1z 1t Ϫ 1x 61. tϪx 63. 1x ϩ h Ϫ 1x h 62. 64. 1x Ϫ 1y 1x ϩ 1y 12 ϩ h ϩ 12 h 65. 032 965 66.

6x3)(4x7)(xϪ5) 31. (a2b3)5 32. (2c4dϪ2)Ϫ3 33. u1ր3u5ր3 34. vϪ1ր5v6ր5 35. (xϪ3)1ր6 36. ( yϪ2ր3)9ր4 37. (49a4bϪ2)1ր2 38. (125aϪ9b12)1ր3 Write the numbers in Problems 39–44 in scientific notation. 39. 45,320,000 Evaluate Problems 67–70, to three significant digits using scientific notation and a calculator. 67. 0513)(80,700,000,000) 68. 000 000 000 704) (835)(635,000,000,000) 69. 000 007 09) 70. 0933)(43,700,000,000) 40. 3,670 41. 066 42. 029 43. 000 000 084 44. 000 497 In Problems 45–50, write each number in standard decimal form.

4 (D) 2 9u 7 (E) Ϫ2 (2x)4 3 3 (F) 2 x ϩ y3 Z Properties of Radicals The exponent properties considered earlier imply the following properties of radicals. Z THEOREM 1 Properties of Radicals For n a natural number greater than 1, and x and y positive real numbers: n 1. 2xn ϭ x n 3 3 2 x ϭx n n 2. 2xy ϭ 2x2y n 3. EXAMPLE 2 x 2x ϭ n By 2y 5 5 5 2 xy ϭ 2 x2 y 4 1 x 4 x ϭ 4 Ay 1y n Simplifying Radicals Simplify: 5 (A) 2 (3x2y)5 ϭ 3x2y (B) 11015 ϭ 150 ϭ 125 ؒ 2 ϭ 12512 ϭ 512 (C) 3 3 x 1 x 1 x ϭ 3 ϭ A 27 3 1 27 3 or MATCHED PROBLEM 1 3 1x 3 2 Simplify: 7 (A) 2 (u2 ϩ v2)7 (B) 1612 (C) x2 B8 3 bar67388_chR_014-035 30 11/02/06 CHAPTER R 00:52 Page 30 BASIC ALGEBRAIC OPERATIONS ZZZ CAUTION ZZZ In general, properties of radicals can be used to simplify terms raised to powers, not sums of terms raised to powers.