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

Review Exercises

Simplify Expressions with Roots

Simplify Expressions with Roots

In the following exercises, simplify.

481.

ⓐ $\sqrt{225} \sqrt{225}$ ⓑ $− \sqrt{16} − \sqrt{16}$

482.

ⓐ $− \sqrt{169} − \sqrt{169}$ ⓑ $\sqrt{−8} \sqrt{−8}$

483.

ⓐ $\sqrt[3]{8} \sqrt[3]{8}$ ⓑ $\sqrt[4]{81} \sqrt[4]{81}$ ⓒ $\sqrt[5]{243} \sqrt[5]{243}$

484.

ⓐ $\sqrt[3]{−512} \sqrt[3]{−512}$ ⓑ $\sqrt[4]{−81} \sqrt[4]{−81}$ ⓒ $\sqrt[5]{−1} \sqrt[5]{−1}$

Estimate and Approximate Roots

In the following exercises, estimate each root between two consecutive whole numbers.

485.

ⓐ $\sqrt{68} \sqrt{68}$ ⓑ $\sqrt[3]{84} \sqrt[3]{84}$

In the following exercises, approximate each root and round to two decimal places.

486.

ⓐ $\sqrt{37} \sqrt{37}$ ⓑ $\sqrt[3]{84} \sqrt[3]{84}$ ⓒ $\sqrt[4]{125} \sqrt[4]{125}$

Simplify Variable Expressions with Roots

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

487.

ⓐ $\sqrt[3]{a^{3}} \sqrt[3]{a^{3}}$
ⓑ $\sqrt[7]{b^{7}} \sqrt[7]{b^{7}}$

488.

ⓐ $\sqrt{a^{14}} \sqrt{a^{14}}$
ⓑ $\sqrt{w^{24}} \sqrt{w^{24}}$

489.

ⓐ $\sqrt[4]{m^{8}} \sqrt[4]{m^{8}}$
ⓑ $\sqrt[5]{n^{20}} \sqrt[5]{n^{20}}$

490.

ⓐ $\sqrt{121 m^{20}} \sqrt{121 m^{20}}$
ⓑ $− \sqrt{64 a^{2}} − \sqrt{64 a^{2}}$

491.

ⓐ $\sqrt[3]{216 a^{6}} \sqrt[3]{216 a^{6}}$
ⓑ $\sqrt[5]{32 b^{20}} \sqrt[5]{32 b^{20}}$

492.

ⓐ $\sqrt{144 x^{2} y^{2}} \sqrt{144 x^{2} y^{2}}$
ⓑ $\sqrt{169 w^{8} y^{10}} \sqrt{169 w^{8} y^{10}}$
ⓒ $\sqrt[3]{8 a^{51} b^{6}} \sqrt[3]{8 a^{51} b^{6}}$

Simplify Radical Expressions

Use the Product Property to Simplify Radical Expressions

In the following exercises, use the Product Property to simplify radical expressions.

493.

$\sqrt{125} \sqrt{125}$

494.

$\sqrt{675} \sqrt{675}$

495.

ⓐ $\sqrt[3]{625} \sqrt[3]{625}$ ⓑ $\sqrt[6]{128} \sqrt[6]{128}$

In the following exercises, simplify using absolute value signs as needed.

496.

ⓐ $\sqrt{a^{23}} \sqrt{a^{23}}$
ⓑ $\sqrt[3]{b^{8}} \sqrt[3]{b^{8}}$
ⓒ $\sqrt[8]{c^{13}} \sqrt[8]{c^{13}}$

497.

ⓐ $\sqrt{80 s^{15}} \sqrt{80 s^{15}}$
ⓑ $\sqrt[5]{96 a^{7}} \sqrt[5]{96 a^{7}}$
ⓒ $\sqrt[6]{128 b^{7}} \sqrt[6]{128 b^{7}}$

498.

ⓐ $\sqrt{96 r^{3} s^{3}} \sqrt{96 r^{3} s^{3}}$
ⓑ $\sqrt[3]{80 x^{7} y^{6}} \sqrt[3]{80 x^{7} y^{6}}$
ⓒ $\sqrt[4]{80 x^{8} y^{9}} \sqrt[4]{80 x^{8} y^{9}}$

499.

ⓐ $\sqrt[5]{−32} \sqrt[5]{−32}$
ⓑ $\sqrt[8]{−1} \sqrt[8]{−1}$

500.

ⓐ $8 + \sqrt{96} 8 + \sqrt{96}$
ⓑ $\frac{2 + \sqrt{40}}{2} \frac{2 + \sqrt{40}}{2}$

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

501.

ⓐ $\sqrt{\frac{72}{98}} \sqrt{\frac{72}{98}}$ ⓑ $\sqrt[3]{\frac{24}{81}} \sqrt[3]{\frac{24}{81}}$ ⓒ $\sqrt[4]{\frac{6}{96}} \sqrt[4]{\frac{6}{96}}$

502.

ⓐ $\sqrt{\frac{y^{4}}{y^{8}}} \sqrt{\frac{y^{4}}{y^{8}}}$ ⓑ $\sqrt[5]{\frac{u^{21}}{u^{11}}} \sqrt[5]{\frac{u^{21}}{u^{11}}}$ ⓒ $\sqrt[6]{\frac{v^{30}}{v^{12}}} \sqrt[6]{\frac{v^{30}}{v^{12}}}$

503.

$\sqrt{\frac{300 m^{5}}{64}} \sqrt{\frac{300 m^{5}}{64}}$

504.

ⓐ $\sqrt{\frac{28 p^{7}}{q^{2}}} \sqrt{\frac{28 p^{7}}{q^{2}}}$
ⓑ $\sqrt[3]{\frac{81 s^{8}}{t^{3}}} \sqrt[3]{\frac{81 s^{8}}{t^{3}}}$
ⓒ $\sqrt[4]{\frac{64 p^{15}}{q^{12}}} \sqrt[4]{\frac{64 p^{15}}{q^{12}}}$

505.

ⓐ $\sqrt{\frac{27 p^{2} q}{108 p^{4} q^{3}}} \sqrt{\frac{27 p^{2} q}{108 p^{4} q^{3}}}$
ⓑ $\sqrt[3]{\frac{16 c^{5} d^{7}}{250 c^{2} d^{2}}} \sqrt[3]{\frac{16 c^{5} d^{7}}{250 c^{2} d^{2}}}$
ⓒ $\sqrt[6]{\frac{2 m^{9} n^{7}}{128 m^{3} n}} \sqrt[6]{\frac{2 m^{9} n^{7}}{128 m^{3} n}}$

506.

ⓐ $\frac{\sqrt{80 q^{5}}}{\sqrt{5 q}} \frac{\sqrt{80 q^{5}}}{\sqrt{5 q}}$
ⓑ $\frac{\sqrt[3]{- 625}}{\sqrt[3]{5}} \frac{\sqrt[3]{- 625}}{\sqrt[3]{5}}$
ⓒ $\frac{\sqrt[4]{80 m^{7}}}{\sqrt[4]{5 m}} \frac{\sqrt[4]{80 m^{7}}}{\sqrt[4]{5 m}}$

Simplify Rational Exponents

Simplify expressions with $a^{\frac{1}{n}} a^{\frac{1}{n}}$

In the following exercises, write as a radical expression.

507.

ⓐ $r^{\frac{1}{2}} r^{\frac{1}{2}}$ ⓑ $s^{\frac{1}{3}} s^{\frac{1}{3}}$ ⓒ $t^{\frac{1}{4}} t^{\frac{1}{4}}$

In the following exercises, write with a rational exponent.

508.

ⓐ $\sqrt{21 p} \sqrt{21 p}$ ⓑ $\sqrt[4]{8 q} \sqrt[4]{8 q}$ ⓒ $4 \sqrt[6]{36 r} 4 \sqrt[6]{36 r}$

In the following exercises, simplify.

509.

ⓐ $625^{\frac{1}{4}} 625^{\frac{1}{4}}$
ⓑ $243^{\frac{1}{5}} 243^{\frac{1}{5}}$
ⓒ $32^{\frac{1}{5}} 32^{\frac{1}{5}}$

510.

ⓐ ${(−1,000)}^{\frac{1}{3}} {(−1,000)}^{\frac{1}{3}}$
ⓑ $− {1,000}^{\frac{1}{3}} − {1,000}^{\frac{1}{3}}$
ⓒ ${(1,000)}^{- \frac{1}{3}} {(1,000)}^{- \frac{1}{3}}$

511.

ⓐ ${(−32)}^{\frac{1}{5}} {(−32)}^{\frac{1}{5}}$
ⓑ ${(243)}^{- \frac{1}{5}} {(243)}^{- \frac{1}{5}}$
ⓒ $− 125^{\frac{1}{3}} − 125^{\frac{1}{3}}$

Simplify Expressions with $a^{\frac{m}{n}} a^{\frac{m}{n}}$

In the following exercises, write with a rational exponent.

512.

ⓐ $\sqrt[4]{r^{7}} \sqrt[4]{r^{7}}$
ⓑ ${(\sqrt[5]{2 p q})}^{3} {(\sqrt[5]{2 p q})}^{3}$
ⓒ $\sqrt[4]{{(\frac{12 m}{7 n})}^{3}} \sqrt[4]{{(\frac{12 m}{7 n})}^{3}}$

In the following exercises, simplify.

513.

ⓐ $25^{\frac{3}{2}} 25^{\frac{3}{2}}$
ⓑ $9^{- \frac{3}{2}} 9^{- \frac{3}{2}}$
ⓒ ${(−64)}^{\frac{2}{3}} {(−64)}^{\frac{2}{3}}$

514.

ⓐ $− 64^{\frac{3}{2}} − 64^{\frac{3}{2}}$
ⓑ $− 64^{- \frac{3}{2}} − 64^{- \frac{3}{2}}$
ⓒ ${(−64)}^{\frac{3}{2}} {(−64)}^{\frac{3}{2}}$

Use the Laws of Exponents to Simplify Expressions with Rational Exponents

In the following exercises, simplify.

515.

ⓐ $6^{\frac{5}{2}} \cdot 6^{\frac{1}{2}} 6^{\frac{5}{2}} \cdot 6^{\frac{1}{2}}$
ⓑ ${(b^{15})}^{\frac{3}{5}} {(b^{15})}^{\frac{3}{5}}$
ⓒ $\frac{w^{\frac{2}{7}}}{w^{\frac{9}{7}}} \frac{w^{\frac{2}{7}}}{w^{\frac{9}{7}}}$

516.

ⓐ $\frac{a^{\frac{3}{4}} \cdot a^{- \frac{1}{4}}}{a^{- \frac{10}{4}}} \frac{a^{\frac{3}{4}} \cdot a^{- \frac{1}{4}}}{a^{- \frac{10}{4}}}$
ⓑ ${(\frac{27 b^{\frac{2}{3}} c^{- \frac{5}{2}}}{b^{- \frac{7}{3}} c^{\frac{1}{2}}})}^{\frac{1}{3}} {(\frac{27 b^{\frac{2}{3}} c^{- \frac{5}{2}}}{b^{- \frac{7}{3}} c^{\frac{1}{2}}})}^{\frac{1}{3}}$

Add, Subtract and Multiply Radical Expressions

Add and Subtract Radical Expressions

In the following exercises, simplify.

517.

ⓐ $7 \sqrt{2} - 3 \sqrt{2} 7 \sqrt{2} - 3 \sqrt{2}$
ⓑ $7 \sqrt[3]{p} + 2 \sqrt[3]{p} 7 \sqrt[3]{p} + 2 \sqrt[3]{p}$
ⓒ $5 \sqrt[3]{x} - 3 \sqrt[3]{x} 5 \sqrt[3]{x} - 3 \sqrt[3]{x}$

518.

ⓐ $\sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} \sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b}$
ⓑ $8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d} 8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d}$

519.

ⓐ $\sqrt{48} + \sqrt{27} \sqrt{48} + \sqrt{27}$
ⓑ $\sqrt[3]{54} + \sqrt[3]{128} \sqrt[3]{54} + \sqrt[3]{128}$
ⓒ $6 \sqrt[4]{5} - \frac{3}{2} \sqrt[4]{320} 6 \sqrt[4]{5} - \frac{3}{2} \sqrt[4]{320}$

520.

ⓐ $\sqrt{80 c^{7}} - \sqrt{20 c^{7}} \sqrt{80 c^{7}} - \sqrt{20 c^{7}}$
ⓑ $2 \sqrt[4]{162 r^{10}} + 4 \sqrt[4]{32 r^{10}} 2 \sqrt[4]{162 r^{10}} + 4 \sqrt[4]{32 r^{10}}$

521.

$3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}} 3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}}$

Multiply Radical Expressions

In the following exercises, simplify.

522.

ⓐ $(5 \sqrt{6}) (− \sqrt{12}) (5 \sqrt{6}) (− \sqrt{12})$
ⓑ $(−2 \sqrt[4]{18}) (− \sqrt[4]{9}) (−2 \sqrt[4]{18}) (− \sqrt[4]{9})$

523.

ⓐ $(3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}})$
ⓑ $(−6 \sqrt[3]{20 a^{2}}) (−2 \sqrt[3]{16 a^{3}}) (−6 \sqrt[3]{20 a^{2}}) (−2 \sqrt[3]{16 a^{3}})$

Use Polynomial Multiplication to Multiply Radical Expressions

In the following exercises, multiply.

524.

ⓐ $\sqrt{11} (8 + 4 \sqrt{11}) \sqrt{11} (8 + 4 \sqrt{11})$
ⓑ $\sqrt[3]{3} (\sqrt[3]{9} + \sqrt[3]{18}) \sqrt[3]{3} (\sqrt[3]{9} + \sqrt[3]{18})$

525.

ⓐ $(3 - 2 \sqrt{7}) (5 - 4 \sqrt{7}) (3 - 2 \sqrt{7}) (5 - 4 \sqrt{7})$
ⓑ $(\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3) (\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3)$

526.

$(2 \sqrt{7} - 5 \sqrt{11}) (4 \sqrt{7} + 9 \sqrt{11}) (2 \sqrt{7} - 5 \sqrt{11}) (4 \sqrt{7} + 9 \sqrt{11})$

527.

ⓐ ${(4 + \sqrt{11})}^{2} {(4 + \sqrt{11})}^{2}$
ⓑ ${(3 - 2 \sqrt{5})}^{2} {(3 - 2 \sqrt{5})}^{2}$

528.

$(7 + \sqrt{10}) (7 - \sqrt{10}) (7 + \sqrt{10}) (7 - \sqrt{10})$

529.

$(\sqrt[3]{3 x} + 2) (\sqrt[3]{3 x} - 2) (\sqrt[3]{3 x} + 2) (\sqrt[3]{3 x} - 2)$

Divide Radical Expressions

Divide Square Roots

In the following exercises, simplify.

530.

ⓐ $\frac{\sqrt{48}}{\sqrt{75}} \frac{\sqrt{48}}{\sqrt{75}}$
ⓑ $\frac{\sqrt[3]{81}}{\sqrt[3]{24}} \frac{\sqrt[3]{81}}{\sqrt[3]{24}}$

531.

ⓐ $\frac{\sqrt{320 m n^{−5}}}{\sqrt{45 m^{−7} n^{3}}} \frac{\sqrt{320 m n^{−5}}}{\sqrt{45 m^{−7} n^{3}}}$
ⓑ $\frac{\sqrt[3]{16 x^{4} y^{−2}}}{\sqrt[3]{−54 x^{−2} y^{4}}} \frac{\sqrt[3]{16 x^{4} y^{−2}}}{\sqrt[3]{−54 x^{−2} y^{4}}}$

Rationalize a One Term Denominator

In the following exercises, rationalize the denominator.

532.

ⓐ $\frac{8}{\sqrt{3}} \frac{8}{\sqrt{3}}$ ⓑ $\sqrt{\frac{7}{40}} \sqrt{\frac{7}{40}}$ ⓒ $\frac{8}{\sqrt{2 y}} \frac{8}{\sqrt{2 y}}$

533.

ⓐ $\frac{1}{\sqrt[3]{11}} \frac{1}{\sqrt[3]{11}}$ ⓑ $\sqrt[3]{\frac{7}{54}} \sqrt[3]{\frac{7}{54}}$ ⓒ $\frac{3}{\sqrt[3]{3 x^{2}}} \frac{3}{\sqrt[3]{3 x^{2}}}$

534.

ⓐ $\frac{1}{\sqrt[4]{4}} \frac{1}{\sqrt[4]{4}}$ ⓑ $\sqrt[4]{\frac{9}{32}} \sqrt[4]{\frac{9}{32}}$ ⓒ $\frac{6}{\sqrt[4]{9 x^{3}}} \frac{6}{\sqrt[4]{9 x^{3}}}$

Rationalize a Two Term Denominator

In the following exercises, simplify.

535.

$\frac{7}{2 - \sqrt{6}} \frac{7}{2 - \sqrt{6}}$

536.

$\frac{\sqrt{5}}{\sqrt{n} - \sqrt{7}} \frac{\sqrt{5}}{\sqrt{n} - \sqrt{7}}$

537.

$\frac{\sqrt{x} + \sqrt{8}}{\sqrt{x} - \sqrt{8}} \frac{\sqrt{x} + \sqrt{8}}{\sqrt{x} - \sqrt{8}}$

Solve Radical Equations

Solve Radical Equations

In the following exercises, solve.

538.

$\sqrt{4 x - 3} = 7 \sqrt{4 x - 3} = 7$

539.

$\sqrt{5 x + 1} = −3 \sqrt{5 x + 1} = −3$

540.

$\sqrt[3]{4 x - 1} = 3 \sqrt[3]{4 x - 1} = 3$

541.

$\sqrt{u - 3} + 3 = u \sqrt{u - 3} + 3 = u$

542.

$\sqrt[3]{4 x + 5} - 2 = −5 \sqrt[3]{4 x + 5} - 2 = −5$

543.

${(8 x + 5)}^{\frac{1}{3}} + 2 = −1 {(8 x + 5)}^{\frac{1}{3}} + 2 = −1$

544.

$\sqrt{y + 4} - y + 2 = 0 \sqrt{y + 4} - y + 2 = 0$

545.

$2 \sqrt{8 r + 1} - 8 = 2 2 \sqrt{8 r + 1} - 8 = 2$

Solve Radical Equations with Two Radicals

In the following exercises, solve.

546.

$\sqrt{10 + 2 c} = \sqrt{4 c + 16} \sqrt{10 + 2 c} = \sqrt{4 c + 16}$

547.

$\sqrt[3]{2 x^{2} + 9 x - 18} = \sqrt[3]{x^{2} + 3 x - 2} \sqrt[3]{2 x^{2} + 9 x - 18} = \sqrt[3]{x^{2} + 3 x - 2}$

548.

$\sqrt{r} + 6 = \sqrt{r + 8} \sqrt{r} + 6 = \sqrt{r + 8}$

549.

$\sqrt{x + 1} - \sqrt{x - 2} = 1 \sqrt{x + 1} - \sqrt{x - 2} = 1$

Use Radicals in Applications

In the following exercises, solve. Round approximations to one decimal place.

550.

Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of 75 square feet. Use the formula $s = \sqrt{A} s = \sqrt{A}$ to find the length of each side of his garden. Round your answer to the nearest tenth of a foot.

551.

Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175 feet. Use the formula $s = \sqrt{24 d} s = \sqrt{24 d}$ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

Use Radicals in Functions

Evaluate a Radical Function

In the following exercises, evaluate each function.

552.

$g (x) = \sqrt{6 x + 1}, g (x) = \sqrt{6 x + 1},$ find
ⓐ $g (4) g (4)$
ⓑ $g (8) g (8)$

553.

$G (x) = \sqrt{5 x - 1}, G (x) = \sqrt{5 x - 1},$ find
ⓐ $G (5) G (5)$
ⓑ $G (2) G (2)$

554.

$h (x) = \sqrt[3]{x^{2} - 4}, h (x) = \sqrt[3]{x^{2} - 4},$ find
ⓐ $h (−2) h (−2)$
ⓑ $h (6) h (6)$

555.

For the function
$g (x) = \sqrt[4]{4 - 4 x}, g (x) = \sqrt[4]{4 - 4 x},$ find
ⓐ $g (1) g (1)$
ⓑ $g (−3) g (−3)$

Find the Domain of a Radical Function

In the following exercises, find the domain of the function and write the domain in interval notation.

556.

$g (x) = \sqrt{2 - 3 x} g (x) = \sqrt{2 - 3 x}$

557.

$F (x) = \sqrt{\frac{x + 3}{x - 2}} F (x) = \sqrt{\frac{x + 3}{x - 2}}$

558.

$f (x) = \sqrt[3]{4 x^{2} - 16} f (x) = \sqrt[3]{4 x^{2} - 16}$

559.

$F (x) = \sqrt[4]{10 - 7 x} F (x) = \sqrt[4]{10 - 7 x}$

Graph Radical Functions

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

560.

$g (x) = \sqrt{x + 4} g (x) = \sqrt{x + 4}$

561.

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

562.

$f (x) = \sqrt[3]{x - 1} f (x) = \sqrt[3]{x - 1}$

563.

$f (x) = \sqrt[3]{x} + 3 f (x) = \sqrt[3]{x} + 3$

Use the Complex Number System

Evaluate the Square Root of a Negative Number

In the following exercises, write each expression in terms of i and simplify if possible.

564.

Add or Subtract Complex Numbers

In the following exercises, add or subtract.

565.

$\sqrt{−50} + \sqrt{−18} \sqrt{−50} + \sqrt{−18}$

566.

$(8 - i) + (6 + 3 i) (8 - i) + (6 + 3 i)$

567.

$(6 + i) - (−2 - 4 i) (6 + i) - (−2 - 4 i)$

568.

$(−7 - \sqrt{−50}) - (−32 - \sqrt{−18}) (−7 - \sqrt{−50}) - (−32 - \sqrt{−18})$

Multiply Complex Numbers

In the following exercises, multiply.

569.

$(−2 - 5 i) (−4 + 3 i) (−2 - 5 i) (−4 + 3 i)$

570.

$−6 i (−3 - 2 i) −6 i (−3 - 2 i)$

571.

$\sqrt{−4} \cdot \sqrt{−16} \sqrt{−4} \cdot \sqrt{−16}$

572.

$(5 - \sqrt{−12}) (−3 + \sqrt{−75}) (5 - \sqrt{−12}) (−3 + \sqrt{−75})$

In the following exercises, multiply using the Product of Binomial Squares Pattern.

573.

${(−2 - 3 i)}^{2} {(−2 - 3 i)}^{2}$

In the following exercises, multiply using the Product of Complex Conjugates Pattern.

574.

$(9 - 2 i) (9 + 2 i) (9 - 2 i) (9 + 2 i)$

Divide Complex Numbers

In the following exercises, divide.

575.

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

576.

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

Simplify Powers of i

In the following exercises, simplify.

577.

$i^{48} i^{48}$

578.

$i^{255} i^{255}$