By Raymond A. Barnett; Michael R. Ziegler; Karl E. Byleen; Dave Sobecki;

Barnett, Ziegler, Byleen, and Sobecki's "College Algebra with Trigonometry" textual content is designed to be person pleasant and to maximise scholar comprehension via emphasizing computational abilities, principles, and challenge fixing in place of mathematical idea. the massive variety of pedagogical units hired during this textual content will consultant a pupil throughout the direction. built-in in the course of the textual content, scholars and teachers will locate Explore-Discuss bins which motivate scholars to imagine seriously approximately mathematical strategies. In every one part, the labored examples are by means of matched difficulties that toughen the concept that being taught. moreover, the textual content comprises an abundance of routines and purposes that might persuade scholars that math turns out to be useful. there's a MathZone web site that includes algorithmic routines, video clips, and different assets accompanies the textual content.

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**Example text**

3 7 3ؒ7 21 ؒ ؍ ؍ 5 8 5ؒ8 40 6. a c aϪc Ϫ ϭ b b b 7 2 7؊2 5 ؊ ؍ ؍ 8 8 8 8 a c a d Ϭ ϭ ؒ b d b c 2 5 2 7 14 ، ؍ ؒ ؍ 3 7 3 5 15 7. a c ad ϩ bc ϩ ϭ b d bd 2 1 2ؒ5؉3ؒ1 13 ؉ ؍ ؍ 3 5 3ؒ5 15 ANSWERS TO MATCHED PROBLEMS 1. (A) Ϫ29ր6 (B) Ϫ17 ր8 (C) 9 ր8 (D) 25ր6 2. (A) Associative (ϩ) (B) Commutative (ϩ) (C) Distributive (D) Identity (ϩ) (E) Inverse (ؒ) 3. (A) Division (Definition 1) (B) Negatives (Theorem 1, part 2) (C) Negatives (Theorem 1, part 4) (D) Negatives (Theorem 1, part 5) (E) Zero (Theorem 2, part 1) R-1 Exercises In Problems 1–16, perform the indicated operations, if defined.

Furthermore, as Figure 1 shows, the calculator uses scientific notation to display the answer, regardless of the manner in which the numbers are entered. 000 000 006 932 62,600,000,000 Z Roots of Real Numbers The solutions of the equation x2 ϭ 64 are called square roots of 64 and the solutions of x3 ϭ 64 are the cube roots of 64. So there are two real square roots of 64 (Ϫ8 and 8) and one real cube root of 64 (4 is a cube root, but Ϫ4 is not). Note that Ϫ64 has no real square root (x2 ϭ Ϫ64 has no real solution because the square of a real number can’t be negative), but Ϫ4 is a cube root of Ϫ64 because (Ϫ4)3 ϭ Ϫ64.

In Problems 51–64, simplify and express answers using positive exponents only. 51. x5xϪ2 52. y6yϪ8 53. (2y)(3y2)(5y4) 54. (6x3)(4x7)(xϪ5) 55. (a2b3)5 56. (2c4dϪ2)Ϫ3 1ր3 5ր3 57. u Ϫ1ր5 6ր5 u 58. v v 60. (49a4bϪ2)1ր2 61. a mϪ2n3 2 b m4nϪ1 w4 Ϫ1ր2 b 9xϪ2 64. a 8aϪ4b3 1ր3 b 27a2bϪ3 63. a Ϫ3 1ր6 59. (x ) 62. a 6mnϪ2 Ϫ3 b 3mϪ1n2 In Problems 65–86, write in simplified radical form. 65. Ϫ1128 66. Ϫ1125 67. 127 Ϫ 5 13 3 3 68. 2 18 ϩ 118 69. 25 Ϫ 225 ϩ 2625 3 3 70. 220 ϩ 240 Ϫ 25 3 3 71. 225 210 72. 16114 4 8 73.