Download e-book for iPad: Algebra and Trigonometry with Analytic Geometry, Classic by Earl Swokowski, Jeffery A. Cole

By Earl Swokowski, Jeffery A. Cole

ISBN-10: 0495559717

ISBN-13: 9780495559719

The newest variation within the hugely revered Swokowski/Cole precalculus sequence keeps the weather that experience made it so well liked by teachers and scholars alike: its exposition is apparent, the time-tested workout units function a number of purposes, its uncluttered structure is beautiful, and the trouble point of difficulties is acceptable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage variation, 12E, successfully prepares scholars for extra classes in arithmetic via its first-class, time-tested challenge units

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N If a is a real number such that 2 a exists, then n (1) a1/n ϭ 2 a m n n m m/n (2) a ϭ ͑ 2 a ͒ ϭ 2 a m/n 1/n m m 1/n (3) a ϭ ͑a ͒ ϭ ͑a ͒ 24 CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA n When evaluating am/n in (2), we usually use ͑ 2 a ͒ ; that is, we take the nth root of a first and then raise that result to the mth power, as shown in the following illustration. m ILLUS TRATION The Exponential Notation a m/n 5 5 3 x3/5 ϭ ͑ 2 x͒ ϭ 2 x 3 x1/3 ϭ 2 x 3 3 3 3 1252/3 ϭ ͑2 125 ͒ ϭ ͑2 5 ͒ ϭ 52 ϭ 25 2 2 32 3/5 32 3 ͑243 ͒ ϭ ͙͑5 243 ͒ ϭ ͙͑5 ͑23 ͒5͒3 ϭ ͑23 ͒3 ϭ 278 The laws of exponents are true for rational exponents and also for irrational exponents, such as 322 or 5␲, considered in Chapter 5.

You may omit this step after you become proficient with such manipulations. (b) When subtracting polynomials, we first remove parentheses, noting that the minus sign preceding the second pair of parentheses changes the sign of each term of that polynomial. 1: Calculator check for Example 2: Store 17 in a memory location and show that the original expression and the final expression both equal 3577. 3 Algebraic Expressions 31 After becoming proficient working problems of the type in Example 2, you may wish to perform the first two steps mentally and proceed directly to the final form.

N If a is a real number such that 2 a exists, then n (1) a1/n ϭ 2 a m n n m m/n (2) a ϭ ͑ 2 a ͒ ϭ 2 a m/n 1/n m m 1/n (3) a ϭ ͑a ͒ ϭ ͑a ͒ 24 CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA n When evaluating am/n in (2), we usually use ͑ 2 a ͒ ; that is, we take the nth root of a first and then raise that result to the mth power, as shown in the following illustration. m ILLUS TRATION The Exponential Notation a m/n 5 5 3 x3/5 ϭ ͑ 2 x͒ ϭ 2 x 3 x1/3 ϭ 2 x 3 3 3 3 1252/3 ϭ ͑2 125 ͒ ϭ ͑2 5 ͒ ϭ 52 ϭ 25 2 2 32 3/5 32 3 ͑243 ͒ ϭ ͙͑5 243 ͒ ϭ ͙͑5 ͑23 ͒5͒3 ϭ ͑23 ͒3 ϭ 278 The laws of exponents are true for rational exponents and also for irrational exponents, such as 322 or 5␲, considered in Chapter 5.

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Algebra and Trigonometry with Analytic Geometry, Classic Edition by Earl Swokowski, Jeffery A. Cole


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