Contents

Preface
1Foundations
- Introduction
- 1.1Use the Language of Algebra
- 1.2Integers
- 1.3Fractions
- 1.4Decimals
- 1.5Properties of Real Numbers
- Chapter Review
  Key Terms
  Key Concepts
- Exercises
  Review Exercises
  Practice Test
2Solving Linear Equations
3Graphs and Functions
4Systems of Linear Equations
5Polynomials and Polynomial Functions
6Factoring
7Rational Expressions and Functions
8Roots and Radicals
9Quadratic Equations and Functions
10Exponential and Logarithmic Functions
11Conics
12Sequences, Series and Binomial Theorem
- Introduction
- 12.1Sequences
- 12.2Arithmetic Sequences
- 12.3Geometric Sequences and Series
- 12.4Binomial Theorem
- Chapter Review
  Key Terms
Answer Key
Index

Practice Test

In the following exercises, simplify using absolute values as necessary.

579.

$\sqrt[3]{125 x^{9}} \sqrt[3]{125 x^{9}}$

580.

$\sqrt{169 x^{8} y^{6}} \sqrt{169 x^{8} y^{6}}$

581.

$\sqrt[3]{72 x^{8} y^{4}} \sqrt[3]{72 x^{8} y^{4}}$

582.

$\sqrt{\frac{45 x^{3} y^{4}}{180 x^{5} y^{2}}} \sqrt{\frac{45 x^{3} y^{4}}{180 x^{5} y^{2}}}$

In the following exercises, simplify. Assume all variables are positive.

583.

ⓐ $216^{- \frac{1}{4}} 216^{- \frac{1}{4}}$ ⓑ $− 49^{\frac{3}{2}} − 49^{\frac{3}{2}}$

584.

$\sqrt{−45} \sqrt{−45}$

585.

$\frac{x^{- \frac{1}{4}} \cdot x^{\frac{5}{4}}}{x^{- \frac{3}{4}}} \frac{x^{- \frac{1}{4}} \cdot x^{\frac{5}{4}}}{x^{- \frac{3}{4}}}$

586.

${(\frac{8 x^{\frac{2}{3}} y^{- \frac{5}{2}}}{x^{- \frac{7}{3}} y^{\frac{1}{2}}})}^{\frac{1}{3}} {(\frac{8 x^{\frac{2}{3}} y^{- \frac{5}{2}}}{x^{- \frac{7}{3}} y^{\frac{1}{2}}})}^{\frac{1}{3}}$

587.

$\sqrt{48 x^{5}} - \sqrt{75 x^{5}} \sqrt{48 x^{5}} - \sqrt{75 x^{5}}$

588.

$\sqrt{27 x^{2}} - 4 x \sqrt{12} + \sqrt{108 x^{2}} \sqrt{27 x^{2}} - 4 x \sqrt{12} + \sqrt{108 x^{2}}$

589.

$2 \sqrt{12 x^{5}} \cdot 3 \sqrt{6 x^{3}} 2 \sqrt{12 x^{5}} \cdot 3 \sqrt{6 x^{3}}$

590.

$\sqrt[3]{4} (\sqrt[3]{16} - \sqrt[3]{6}) \sqrt[3]{4} (\sqrt[3]{16} - \sqrt[3]{6})$

591.

$(4 - 3 \sqrt{3}) (5 + 2 \sqrt{3}) (4 - 3 \sqrt{3}) (5 + 2 \sqrt{3})$

592.

$\frac{\sqrt[3]{128}}{\sqrt[3]{54}} \frac{\sqrt[3]{128}}{\sqrt[3]{54}}$

593.

$\frac{\sqrt{245 x y^{−4}}}{\sqrt{45 x^{−4} y^{3}}} \frac{\sqrt{245 x y^{−4}}}{\sqrt{45 x^{−4} y^{3}}}$

594.

$\frac{1}{\sqrt[3]{5}} \frac{1}{\sqrt[3]{5}}$

595.

$\frac{3}{2 + \sqrt{3}} \frac{3}{2 + \sqrt{3}}$

596.

$\sqrt{−4} \cdot \sqrt{−9} \sqrt{−4} \cdot \sqrt{−9}$

597.

$−4 i (−2 - 3 i) −4 i (−2 - 3 i)$

598.

$\frac{4 + i}{3 - 2 i} \frac{4 + i}{3 - 2 i}$

599.

$i^{172} i^{172}$

In the following exercises, solve.

600.

$\sqrt{2 x + 5} + 8 = 6 \sqrt{2 x + 5} + 8 = 6$

601.

$\sqrt{x + 5} + 1 = x \sqrt{x + 5} + 1 = x$

602.

$\sqrt[3]{2 x^{2} - 6 x - 23} = \sqrt[3]{x^{2} - 3 x + 5} \sqrt[3]{2 x^{2} - 6 x - 23} = \sqrt[3]{x^{2} - 3 x + 5}$

In the following exercise, ⓐ find the domain of the function ⓑ graph the function ⓒ use the graph to determine the range.

603.

$g (x) = \sqrt{x + 2} g (x) = \sqrt{x + 2}$