# Algebra and trigonometry, 2nd Edition by James Stewart

By James Stewart

This most sensible promoting writer group explains suggestions easily and obviously, with no glossing over tricky issues. challenge fixing and mathematical modeling are brought early and bolstered all through, in order that while scholars end the direction, they've got an excellent origin within the rules of mathematical considering. This accomplished, flippantly paced ebook presents whole insurance of the functionality proposal and integrates big graphing calculator fabrics that support scholars strengthen perception into mathematical principles. The authors' cognizance to aspect and readability, as in James Stewart's market-leading Calculus textual content, is what makes this article the industry chief.

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**Additional resources for Algebra and trigonometry, 2nd Edition **

**Example text**

A) 11, 32 പ 32, 74 (b) 11, 32 ʜ 32, 74 Solution (a) The intersection of two intervals consists of the numbers that are in both intervals. Therefore 11, 32 പ 32, 74 ϭ 5x 0 1 Ͻ x Ͻ 3 and 2 Յ x Յ 76 ϭ 5x 0 2 Յ x Ͻ 36 ϭ 32, 32 This set is illustrated in Figure 7. (b) The union of two intervals consists of the numbers that are in either one interval or the other (or both). Therefore 11, 32 ʜ 32, 74 ϭ 5x 0 1 Ͻ x Ͻ 3 or 2 Յ x Յ 76 ϭ 5x 0 1 Ͻ x Յ 76 ϭ 11, 74 This set is illustrated in Figure 8. 0001 17 1 Figure 8 11, 3 2 ʜ 32, 74 ϭ 11, 74 7 ■ Absolute Value and Distance | _3 |=3 _3 Figure 9 | 5 |=5 0 5 The absolute value of a number a, denoted by 0 a 0 , is the distance from a to 0 on the real number line (see Figure 9).

Proof of Law 4 If n is a positive integer, we have 1ab2 n ϭ 1ab2 1ab2 . . 1ab2 ϭ 1a # a # . . # a2 # 1b # b # . . # b2 ϭ a n b n 144424443 n factors 1442443 n factors 1442443 n factors Here we have used the Commutative and Associative Properties repeatedly. If n Յ 0, Law 4 can be proved using the definition of negative exponents. ■ You are asked to prove Laws 2 and 5 in Exercise 76. 24 CHAPTER P Prerequisites Example 3 Using Laws of Exponents (a) x 4x 7 ϭ x 4ϩ7 ϭ x 11 Law 1: a ma n ϭ a mϩn (b) y 4y Ϫ7 ϭ y 4Ϫ7 ϭ y Ϫ3 ϭ 1 y3 c9 ϭ c 9Ϫ5 ϭ c 4 c5 # (d) 1b 4 2 5 ϭ b 4 5 ϭ b 20 Law 2: a m/a n ϭ a mϪn (c) Law 3: (a m) n ϭ a mn (e) 13x2 3 ϭ 33x 3 ϭ 27x 3 Law 4: (ab)n ϭ a nb n x 5 x5 x5 (f) a b ϭ 5 ϭ 2 32 2 Example 4 Law 1: a ma n ϭ a mϩn Law 5: (a/b) n ϭ a n/b n ■ Simplifying Expressions with Exponents Simplify: x 3 y 2x 4 (b) a b a b z y (a) 12a 3b 2 2 13ab 4 2 3 Solution (a) 12a 3b 2 2 13ab 4 2 3 ϭ 12a 3b 2 2 333a 3 1b 4 2 3 4 ϭ 12a 3b 2 2 127a 3b 12 2 ϭ 122 1272a 3a 3b 2b 12 Law 4: (ab)n ϭ a nb n Law 3: (a m)n ϭ a mn Group factors with the same base Apago PDF ϭ 54a Enhancer b Law 1: a a 6 14 x 3 y 2x 4 x 3 1y 2 2 4x 4 (b) a b a b ϭ 3 z y y z4 ϭ x 3 y 8x 4 y 3 z4 ϭ 1x 3x 4 2 a ϭ x 7y 5 z4 m n ϭ a mϩn Laws 5 and 4 Law 3 y8 1 b y 3 z4 Group factors with the same base Laws 1 and 2 ■ When simplifying an expression, you will find that many different methods will lead to the same result; you should feel free to use any of the rules of exponents to arrive at your own method.

000028536 20. ■ A 14 B Ϫ2 32 # 4Ϫ2 # 5 2Ϫ4 # 33 # 25 19. A 131 B 0 A 23 B 6 A 49 B Ϫ3 23–32 ■ ■ Write each number in decimal notation. 59. 19 ϫ 10 5 60. 721 ϫ 108 61. 670 ϫ 10Ϫ8 62. 999 ϫ 10Ϫ9 63. 1 ϫ 1014 64. 6 ϫ 1012 65. 55 ϫ 10Ϫ3 66. 257 ϫ 10Ϫ10 67–68 ■ Write the number indicated in each statement in scientific notation. 67. (a) A light-year, the distance that light travels in one year, is about 5,900,000,000,000 mi. 0000000000004 cm. (c) A drop of water contains more than 33 billion billion molecules.