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

The most recent version 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 obvious, the time-tested workout units characteristic various functions, its uncluttered format is attractive, and the trouble point of difficulties is suitable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage variation, 12E, successfully prepares scholars for additional classes in arithmetic via its first-class, time-tested challenge units.

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Some special cases are listed in the following chart. 2 Exponents and Radicals 23 Rationalizing Denominators of Quotients (a > 0) Factor in denominator Multiply numerator and denominator by Resulting factor 2a 2a 2 a 2 a ϭ 2 a2 ϭ a 3 7 2 a 2 a2 ϭ 2 a3 ϭ a 3 2a 3 2 a2 7 2a 3 3 2 a 2 a ϭ 2 a7 ϭ a 7 2a 3 4 3 7 4 7 The next example illustrates this technique. EXAMPLE 4 Rationalizing denominators ͱ Rationalize each denominator: 1 1 (a) (b) 3 (c) 25 2x 2 3 (d) ͱ 5 x y2 SOLUTION (a) (b) (c) (d) 1 ͙5 1 3 x ͙ ͱ ͱ 5 ෇ 1 ͙5 ͙5 ͙5 ෇ ෇ 2 5 ͙5 ͙5 ͙5 ෇ 3 2 3 2 3 2 1 ͙ x x x ͙ ͙ ෇ ෇ 3 3 2 3 3 x ͙x ͙x ͙x 2 ͙2 ͙2 ͙3 ͙2 и 3 ͙6 ෇ ෇ ෇ ෇ 3 3 ͙3 ͙3 ͙3 ͙32 5 5 5 3 5 5 x x x ͙ y xy 3 ͙ xy 3 ͙ ͙ ͙ 2 ෇ 5 2 ෇ 5 2 5 3 ෇ 5 5 ෇ y y ͙y ͙y ͙y ͙y L If we use a calculator to find decimal approximations of radicals, there is no advantage in rationalizing denominators, such as 1͞ 25 ϭ 25͞5 or 22͞3 ϭ 26͞3, as we did in Example 4(a) and (c).

000 005 5 (c) 24,900,000 Exer. 51–52: Express the number in decimal form. 000 000 000 000 000 000 000 001 7 gram. Express this number in scientific form. 1 ϫ 10Ϫ31 kilogram. Express this number in decimal form. 55 Light year In astronomy, distances to stars are measured in light years. One light year is the distance a ray of light travels in one year. If the speed of light is approximately 186,000 miles per second, estimate the number of miles in one light year. 56 Milky Way galaxy (a) Astronomers have estimated that the Milky Way galaxy contains 100 billion stars.

We next use radicals to define rational exponents. Definition of Rational Exponents Let m͞n be a rational number, where n is a positive integer greater than 1. 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.