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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Chapter Review
      1. Key Terms
      2. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Chapter Review
      1. Key Terms
      2. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index

Be Prepared

9.1

8181 8181 8181

9.2

3.85 3.85

9.3

100100 100100.

9.4

5 11 5 11

9.5

n 6 n 6

9.6

1 q 8 1 q 8

9.7

12x12x 5m+5n5m+5n

9.8

5 x 2 x 5 x 2 x

9.9

24 u v 24 u v

9.10

72 42 n 72 42 n

9.11

8 + 2 a + a 2 8 + 2 a + a 2

9.12

30 48 30 48

9.13

5 5

9.14

49 9 x 2 49 9 x 2

9.15

33 8181

9.16

22 22

9.17

n = 2 or n = 4 n = 2 or n = 4

9.18

y 9 y 9

9.19

n 12 n 12

9.20

x 5 x 5

9.21

53 60 53 60

9.22

64 x 6 y 15 64 x 6 y 15

9.23

1 125 1 125

Try It

9.1

−7−7 1515

9.2

88 −11−11

9.3

not a real number −9−9

9.4

−7−7 not a real number

9.5

7 5

9.6

17 2323

9.7

6 < 38 < 7 6 < 38 < 7

9.8

9 < 84 < 10 9 < 84 < 10

9.9

3.32 3.32

9.10

3.61 3.61

9.11

y4y4 z6z6

9.12

m2m2 b5b5

9.13

8 x 8 x

9.14

13 y 13 y

9.15

−11 y −11 y

9.16

−10 p −10 p

9.17

10 a b 10 a b

9.18

15 m n 15 m n

9.19

7 x 15 7 x 15

9.20

9 w 18 9 w 18

9.21

13 x 5 y 7 13 x 5 y 7

9.22

12 p 6 q 10 12 p 6 q 10

9.23

4 3 4 3

9.24

3 5 3 5

9.25

12 2 12 2

9.26

12 3 12 3

9.27

b 2 b b 2 b

9.28

p 4 p p 4 p

9.29

4 x 3 x 4 x 3 x

9.30

7 v 4 v 7 v 4 v

9.31

4 y 2 2 y 4 y 2 2 y

9.32

5 a 4 3 a 5 a 4 3 a

9.33

7 a 3 b 2 2 a b 7 a 3 b 2 2 a b

9.34

6 m 4 n 5 5 m n 6 m 4 n 5 5 m n

9.35

5 + 5 3 5 + 5 3

9.36

2 + 7 2 2 + 7 2

9.37

2 3 2 3

9.38

2 5 2 5

9.39

5 4 5 4

9.40

7 9 7 9

9.41

5 4 5 4

9.42

7 9 7 9

9.43

a a

9.44

x 2 x 2

9.45

5 x 2 5 x 2

9.46

6 z 6 z

9.47

19 7 19 7

9.48

2 7 9 2 7 9

9.49

2 p 6 p 7 2 p 6 p 7

9.50

2 x 2 3 x 5 2 x 2 3 x 5

9.51

4 m 5 m n 3 4 m 5 m n 3

9.52

3 u 3 6 u v 4 3 u 3 6 u v 4

9.53

8 x 2 3 8 x 2 3

9.54

2 a 2 5 2 a 2 5

9.55

5 y x 6 5 y x 6

9.56

4 m 3 5 n 3 5 n 4 m 3 5 n 3 5 n

9.57

2 2

9.58

−4 3 −4 3

9.59

9 x 9 x

9.60

8 u 8 u

9.61

7 p 6 q 7 p 6 q

9.62

6 a 3 b 6 a 3 b

9.63

9 11 9 11

9.64

11 10 11 10

9.65

5 + 2 6 5 + 2 6

9.66

−5 7 + 2 5 −5 7 + 2 5

9.67

−2 7 x −2 7 x

9.68

3 y 3 y

9.69

−2 5 x y −2 5 x y

9.70

0 0

9.71

9 2 9 2

9.72

7 3 7 3

9.73

2 2

9.74

5 5

9.75

6 3 6 3

9.76

−15 5 −15 5

9.77

3 3

9.78

0 0

9.79

14 15 2 14 15 2

9.80

1 12 5 1 12 5

9.81

m 3 2 m m 3 2 m

9.82

p 3 p p 3 p

9.83

20 x 2 12 x 3 20 x 2 12 x 3

9.84

28 y 3 24 y 2 28 y 3 24 y 2

9.85

10 x 3 10 x 3

9.86

−5 x 2 −5 x 2

9.87

3232 362362

9.88

5252 902902

9.89

12 15 12 15

9.90

27 2 27 2

9.91

3x223x22 10y2y10y2y

9.92

2x332x33 6y2y6y2y

9.93

144 x 3 10 144 x 3 10

9.94

144 y 2 5 y 144 y 2 5 y

9.95

12 1515

9.96

16 20

9.97

330 200

9.98

210 96

9.99

625625 23362336

9.100

12+6612+66 7+727+72

9.101

18+618+6 6+1226+122

9.102

−40+42−40+42 27+14327+143

9.103

−3 + 2 6 −3 + 2 6

9.104

−2 + 2 10 −2 + 2 10

9.105

−66 + 15 7 −66 + 15 7

9.106

41 14 11 41 14 11

9.107

1 + 9 21 1 + 9 21

9.108

−12 20 3 −12 20 3

9.109

12 + 8 m 15 m 12 + 8 m 15 m

9.110

10 47 n 15 n 10 47 n 15 n

9.111

102+202102+202 55+6655+66

9.112

4112541125 12136101213610

9.113

4 + 20 m + 25 m 4 + 20 m + 25 m

9.114

9 24 n + 16 n 9 24 n + 16 n

9.115

1 1

9.116

−4 −4

9.117

−11 −11

9.118

−159 −159

9.119

2 2 2 2

9.120

3 3 3 3

9.121

4 10 5 4 10 5

9.122

2 3 4 2 3 4

9.123

2 3 2 3

9.124

4 3 4 3

9.125

r 2 r 2

9.126

p 2 7 p 2 7

9.127

5 s 8 5 s 8

9.128

5 q 2 6 5 q 2 6

9.129

9 x 2 y 2 9 x 2 y 2

9.130

10 n 3 m 10 n 3 m

9.131

5 3 3 5 3 3

9.132

6 5 5 6 5 5

9.133

5 2 5 2

9.134

3 3 4 3 3 4

9.135

14 6 14 6

9.136

6 8 6 8

9.137

1 3 1 3

9.138

5 5 5 5

9.139

2 ( 2 3 ) 1 2 ( 2 3 ) 1

9.140

5 ( 5 3 ) 22 5 ( 5 3 ) 22

9.141

3 ( 1 + 5 ) 4 3 ( 1 + 5 ) 4

9.142

4 + 6 5 4 + 6 5

9.143

5 ( x 2 ) x 2 5 ( x 2 ) x 2

9.144

10 ( y + 3 ) y 3 10 ( y + 3 ) y 3

9.145

( p + 2 ) p 2 2 ( p + 2 ) p 2 2

9.146

( q 10 ) q 10 2 ( q 10 ) q 10 2

9.147

no yesyes

9.148

no yesyes

9.149

10 10

9.150

7 7

9.151

23 3 23 3

9.152

3 10 3 10

9.153

1 3 1 3

9.154

3 5 3 5

9.155

no solution no solution

9.156

no solution no solution

9.157

2 , 3 2 , 3

9.158

5 , 6 5 , 6

9.159

7 7

9.160

3 3

9.161

127 2 127 2

9.162

311 3 311 3

9.163

no solution

9.164

no solution

9.165

no solution no solution

9.166

no solution no solution

9.167

no solution no solution

9.168

no solution no solution

9.169

19.2 feet 19.2 feet

9.170

52.0 cm 52.0 cm

9.171

9 seconds 9 seconds

9.172

3.5 seconds 3.5 seconds

9.173

42.7 miles per hour 42.7 miles per hour

9.174

54.1 miles per hour 54.1 miles per hour

9.175

3 4 3

9.176

10 2 2

9.177

−5−5 not real −2−2

9.178

−6−6 not real −4−4

9.179

|b||b| ww |m||m| qq

9.180

|y||y| pp |z||z| qq

9.181

u3u3 v5v5

9.182

c4c4 d4d4

9.183

3x93x9 3|q7|3|q7|

9.184

5p35p3 3q53q5

9.185

|y|y24|y|y24 zz23zz23

9.186

pp35pp35 q2q6q2q6

9.187

343343 244244

9.188

553553 394394

9.189

3p32p33p32p3 2q24q242q24q24

9.190

4m32m234m32m23 3|n|2n343|n|2n34

9.191

−343−343 not realnot real

9.192

−553−553 not realnot real

9.193

|x||x| y3y3

9.194

m2m2 n2n2

9.195

26632663 3|m|2m243|m|2m24

9.196

−4−4 3|n|243|n|24

9.197

3c34c3d23c34c3d2 2x2|y|5x2y42x2|y|5x2y4

9.198

2r5s32r5s3 3m32m24|n3|3m32m24|n3|

9.199

23x523x5 293293

9.200

210y4210y4 23262326

9.201

3333 624624

9.202

2323 525525

9.203

2y4y23+3y24y232y4y23+3y24y23 3r23r34+4r23r243r23r34+4r23r24

9.204

2z25z3+3z5z32z25z3+3z5z3 2|s3|5s4+4|s|5s242|s3|5s4+4|s|5s24

9.205

tt m3m3 r4r4

9.206

bb z3z3 p4p4

9.207

s12s12 x13x13 b14b14

9.208

v12v12 p13p13 p14p14

9.209

(10m)12(10m)12 (3n)15(3n)15 (486y)14(486y)14

9.210

(3k)17(3k)17 (5j)14(5j)14 (1024a)13(1024a)13

9.211

6 2 2

9.212

10 3 3

9.213

−5−5 −5−5 1515

9.214

−2−2 −2−2 1212

9.215

not real −8−8 1818

9.216

not real −4−4 1414

9.217

x52x52 z34z34 y25y25

9.218

a25a25 b73b73 m54m54

9.219

8 9 125

9.220

32 729 8

9.221

132132 17291729 1818

9.222

1818 1919 11251125

9.223

−64−64 164164 not a real number

9.224

−729−729 17291729 not a real number

9.225

9 y3y3 m

9.226

25 z n

9.227

p2p2 q6q6 x8x8

9.228

r10r10 s9s9 m2m2

9.229

u v15v15 1x1x

9.230

c2c2 1m1m 1d1d

9.231

8x158x15 4y294y29

9.232

64m1264m12 729n35729n35

9.233

m2m2 n3n3

9.234

u3u3 v5v5

Section 9.1 Exercises

1.

6

3.

8

5.

3

7.

10

9.

−2 −2

11.

−1 −1

13.

not a real number

15.

not a real number

17.

5

19.

7

21.

8 < 70 < 9 8 < 70 < 9

23.

14 < 200 < 15 14 < 200 < 15

25.

4.36

27.

7.28

29.

y y

31.

a 7 a 7

33.

7 x 7 x

35.

11 m 10 11 m 10

37.

9 x 18 9 x 18

39.

−9 x 9 −9 x 9

41.

−8 a −8 a

43.

12 x y 12 x y

45.

13 w 4 y 5 13 w 4 y 5

47.

3 c 4 d 6 3 c 4 d 6

49.

25 centimeters

51.

Answers will vary.

Section 9.2 Exercises

53.

3 3 3 3

55.

5 5 5 5

57.

10 2 10 2

59.

15 2 15 2

61.

20 2 20 2

63.

15 3 15 3

65.

x 3 x x 3 x

67.

p p p p

69.

m 6 m m 6 m

71.

r 12 r r 12 r

73.

7 n 8 n 7 n 8 n

75.

9 r 7 r 9 r 7 r

77.

7 m 2 2 m 7 m 2 2 m

79.

5 r 6 5 r 5 r 6 5 r

81.

10 p 6 2 p 10 p 6 2 p

83.

11 m 11 2 m 11 m 11 2 m

85.

7 m 3 n 5 3 m n 7 m 3 n 5 3 m n

87.

5 r 6 s 4 3 r s 5 r 6 s 4 3 r s

89.

10 p 4 q 5 3 p q 10 p 4 q 5 3 p q

91.

11 m 6 n 10 2 m n 11 m 6 n 10 2 m n

93.

5 + 2 3 5 + 2 3

95.

1 + 3 5 1 + 3 5

97.

5 6 5 6

99.

1 + 10 1 + 10

101.

7 8 7 8

103.

11 4 11 4

105.

6 7 6 7

107.

3 5 3 5

109.

x 2 x 2

111.

1 y 2 1 y 2

113.

10 x 2 10 x 2

115.

4 p 4 4 p 4

117.

6 35 6 35

119.

2 5 9 2 5 9

121.

4 x 3 6 x 11 4 x 3 6 x 11

123.

5 m 2 3 m 4 5 m 2 3 m 4

125.

7 r 2 2 r 10 7 r 2 2 r 10

127.

2 q 3 7 15 2 q 3 7 15

129.

5 r 4 3 r s 4 5 r 4 3 r s 4

131.

2 p 3 7 p q 2 p 3 7 p q

133.

5 x 3 5 x 3

135.

11 p p 9 11 p p 9

137.

4 x y 3 4 x y 3

139.

1 2 p q p 1 2 p q p

141.

17.0feet17.0feet 12.0feet12.0feet

143.

Answers will vary.

Section 9.3 Exercises

145.

3 2 3 2

147.

9 5 9 5

149.

7 7

151.

9 y 9 y

153.

−3 a −3 a

155.

7 c 7 c

157.

8 a 2 b 8 a 2 b

159.

5 m + n 5 m + n

161.

13 7 13 7

163.

−3 11 −3 11

165.

−5 3 + 7 5 −5 3 + 7 5

167.

8 2 3 5 8 2 3 5

169.

4 2 a 4 2 a

171.

3 c 3 c

173.

4 3 a b 4 3 a b

175.

p q p q

177.

9 2 9 2

179.

5 5

181.

−2 3 −2 3

183.

7 3 7 3

185.

−8 2 −8 2

187.

16 3 16 3

189.

5 2 5 2

191.

5 5

193.

3 3

195.

11 12 2 11 12 2

197.

a 2 2 a a 2 2 a

199.

2 c 3 5 c 2 c 3 5 c

201.

36 p 2 5 42 p 2 2 36 p 2 5 42 p 2 2

203.

10 r 4 2 + 12 r 4 6 10 r 4 2 + 12 r 4 6

205.

14 x 5 14 x 5

207.

4 y 2 4 y 2

209.

6 2 6 2

211.

2 k 2 7 2 k 2 7

213.

2 3 2 3

215.

2 2

217.

13 13

219.

a 2 5 a a 2 5 a

221.

19 19 19 19

223.

5 3 5 3

225.

3 3

227.

8 x 6 8 x 6

229.

124.5 inches 124.5 inches

231.

Answers will vary.

Section 9.4 Exercises

233.

44 186186

235.

7272 160

237.

30 3 30 3

239.

−18 6 −18 6

241.

−30 2 −30 2

243.

28 2 28 2

245.

5y235y23 6n2n6n2n

247.

8y328y32 11s3s11s3s

249.

40 b 2 3 40 b 2 3

251.

144 d 4 144 d 4

253.

54 y 4 y 54 y 4 y

255.

−96 k 5 k −96 k 5 k

257.

11 21

259.

23 3

261.

−234 180

263.

10521052 56

265.

2441124411 52265226

267.

−14711−14711 67726772

269.

44+81144+811 1515

271.

18521852 21732173

273.

60 + 2 3 60 + 2 3

275.

52 + 3 2 52 + 3 2

277.

27 9 7 27 9 7

279.

−62 + 55 5 −62 + 55 5

281.

41 + 7 55 41 + 7 55

283.

−81 + 44 78 −81 + 44 78

285.

18 + 7 w w 18 + 7 w w

287.

66 + 73 n + 15 n 66 + 73 n + 15 n

289.

27+81127+811 2912529125

291.

351010351010 82+48282+482

293.

97

295.

39

297.

−127 −127

299.

33

301.

−24 3 −24 3

303.

−210 3 −210 3

305.

7 y 3 5 7 y 3 5

307.

29 29

309.

29 7 17 29 7 17

311.

4.6feet4.6feet 21sq. feet21sq. feet

313.

31.9squareyards31.9squareyards

315.

when squaring a negative, it becomes a positive since the negative is not included in the parenthesis, it is not squared, and remains negative

Section 9.5 Exercises

317.

3 2 3 2

319.

2 2 3 2 2 3

321.

1 2 2 4 1 2 2 4

323.

2 + 5 2 2 + 5 2

325.

4 5 4 5

327.

4 3 4 3

329.

2x22x2 10m2710m27

331.

5 r 6 5 r 6

333.

3 p 102 17 q 2 3 p 102 17 q 2

335.

8 n 3 m 3 8 n 3 m 3

337.

2 2 2 2

339.

1 + 5 3 1 + 5 3

341.

4 5 4 5

343.

y 3 13 y 3 13

345.

5 6 3 5 6 3

347.

6 7 7 6 7 7

349.

3 13 13 3 13 13

351.

10 3 10 3

353.

4 5 45 4 5 45

355.

3 3 2 3 3 2

357.

15 10 15 10

359.

70 20 70 20

361.

133 35 133 35

363.

3(311)−23(311)−2 −2(1+5)−2(1+5)

365.

5(56)195(56)19 3(3+7)3(3+7)

367.

3 ( m + 5 ) m 5 3 ( m + 5 ) m 5

369.

2 ( x + 6 ) x 6 2 ( x + 6 ) x 6

371.

( r + 5 ) r 5 2 ( r + 5 ) r 5 2

373.

5 y 2 x 5 y 2 x

375.

3 5 3 5

377.

2 3 9 2 3 9

379.

3 ( 5 5 ) 20 3 ( 5 5 ) 20

381.

2 ( x + 3 ) x 3 2 ( x + 3 ) x 3

383.

( x + 2 2 ) x 8 2 ( x + 2 2 ) x 8 2

385.

5 10 4 seconds 5 10 4 seconds

387.

Answers will vary.

Section 9.6 Exercises

389.

yesyes nono

391.

no yes

393.

3

395.

14

397.

14

399.

17 17

401.

13 5 13 5

403.

5 2 5 2

405.

no solution no solution

407.

no solution no solution

409.

10,1110,11 55

411.

8,98,9 1111

413.

3 3

415.

5 5

417.

not a real number

419.

1 4 1 4

421.

no solutionno solution 57165716

423.

no solutionno solution 6

425.

no solution

427.

36

429.

15

431.

11.4 feet 11.4 feet

433.

8 seconds 8 seconds

435.

15.8 seconds 15.8 seconds

437.

72 miles per hour 72 miles per hour

439.

53.0 miles per hour 53.0 miles per hour

441.

Answers will vary.

Section 9.7 Exercises

443.

33 22 33

445.

55 66 44

447.

−4−4 not realnot real −3−3

449.

−8−8 not a real number −1−1

451.

aa |b||b|

453.

|k||k| |p||p|

455.

a2a2 b9b9

457.

r2r2 s10s10

459.

−2c3−2c3 5d55d5

461.

2r22r2 3s63s6

463.

uu25uu25 vv56vv56

465.

pp35pp35 q2q23q2q23

467.

553553 226226

469.

554554 333333

471.

2a3a252a3a25 5b3b35b3b3

473.

8pp238pp23 3q4q343q4q34

475.

−325−325 not realnot real

477.

−2−2 not realnot real

479.

dd |m||m|

481.

r3r3 |c3||c3|

483.

−5−5 2mm242mm24

485.

363363 2|r|2r342|r|2r34

487.

2r23rs352r23rs35 2u2uv362u2uv36

489.

5u35u3v5u35u3v 3c59c4d23c59c4d2

491.

215q3215q3 −4274−4274

493.

.

.
495.

223223 −234−234

497.

334+524334+524 13231323

499.

2b10b23+3b1032b10b23+3b103 2v210v2445v342v210v2445v34

501.

2 2

503.

| b | | b |

505.

5 d 5 5 d 5

507.

s 2 s 2 4 s 2 s 2 4

509.

2 y 3 y 2 4 2 y 3 y 2 4

511.

not real not real

513.

2 x 2 x 5 2 x 2 x 5

515.

2 u 2 u v 3 6 2 u 2 u v 3 6

517.

2 2 4 2 2 4

519.

3 u 6 u 3 4 + 4 3 u 3 4 3 u 6 u 3 4 + 4 3 u 3 4

521.

5 5

523.

Answers may vary.

Section 9.8 Exercises

525.

rr s3s3 t4t4

527.

g7g7 h5h5 j25j25

529.

r18r18 s110s110 t14t14

531.

u15u15 v12v12 w116w116

533.

(5x)14(5x)14 (9y)18(9y)18 7(3z)157(3z)15

535.

(25a)13(25a)13 (3b)12(3b)12 (40c)110(40c)110

537.

5 3 2

539.

6 2 3

541.

−3−3 −3−3 1313

543.

−10−10 −10−10 110110

545.

not a real number −7−7 1717

547.

not a real number 11 −1−1

549.

−2−2 1313
−5−5

551.

r74r74 s35s35 t73t73

553.

a13a13 b52b52 c53c53

555.

100 125 8

557.

64 3125 256

559.

32,768 17291729 181181

561.

1000 116,807116,807 not a real number

563.

−512−512
15121512 not a real number

565.

−343−343 13431343 not a real number

567.

216 nn q3q3

569.

100 x2x2 y4y4

571.

a2a2 b9b9
cc

573.

h8h8 k9k9 j14j14

575.

ss z2z2 1w1w

577.

uu rr 1n1n

579.

3r153r15 2s1142s114

581.

9m129m12 125n2125n2

583.

r2sr2s u3v4u3v4

585.

r8s5r8s5 u8v4u8v4

587.

a3a3 b4b4

589.

mm n2n2

591.

n n

593.

b 6 b 6

595.

1 z 2 1 z 2

597.

2 s 1 10 2 s 1 10

599.

u 2 v 3 u 2 v 3

601.

15.6 feet

603.

8 seconds

605.

Answers will vary.

Review Exercises

607.

12

609.

−9 −9

611.

not a real number

613.

17

615.

12 < 155 < 13 12 < 155 < 13

617.

7.55

619.

8 b 8 b

621.

15 m n 15 m n

623.

7 y 7 y

625.

11 c d 11 c d

627.

7 2 7 2

629.

y 9 y y 9 y

631.

6 n 6 n 6 n 6 n

633.

5 n 3 6 n 5 n 3 6 n

635.

6 r 2 s 3 r s 6 r 2 s 3 r s

637.

1 + 2 1 + 2

639.

3 2 3 2

641.

y 2 y 2

643.

6 q 2 6 q 2

645.

26 13 26 13

647.

3 r 2 r 2 3 r 2 r 2

649.

2 r s 3 r 5 2 r s 3 r 5

651.

12 5 12 5

653.

4 m 4 m

655.

11 13 + 2 3 11 13 + 2 3

657.

3 3 r s 5 r s 3 3 r s 5 r s

659.

5 2 5 2

661.

9 3 9 3

663.

0 0

665.

17 n 2 2 17 n 2 2

667.

24 7 24 7

669.

180 y 2 180 y 2

671.

8

673.

50

675.

20 10 7 20 10 7

677.

13 2 2 13 2 2

679.

5 13 x 6 x 5 13 x 6 x

681.

1 + 12 p + 36 p 1 + 12 p + 36 p

683.

−19 −19

685.

3 2 3 2

687.

4 3 4 3

689.

y 2 10 y 2 10

691.

2 15 3 2 15 3

693.

5 3 5 3

695.

21 14 21 14

697.

16 12 3 −11 16 12 3 −11

699.

−8 4 5 −8 4 5

701.

2 p 6 p 3 2 p 6 p 3

703.

5

705.

7 2 7 2

707.

4 and 5

709.

13

711.

43 2 43 2

713.

0

715.

1 16 1 16

717.

11

719.

7.5 seconds

721.

2 4

723.

dd |v||v|

725.

2x22x2 2y22y2

727.

dd mm611mm611

729.

2c2c352c2c35 2d3d342d3d34

731.

−543−543 not a real number

733.

w 3 w 3 w 3 w 3

735.

3 z 2 3 z 2

737.

2 20 5 2 20 5

739.

2 2 4 2 2 4

741.

2 t 3 t 3 5 + 3 2 t 4 5 2 t 3 t 3 5 + 3 2 t 4 5

743.
.
745.

v 1 6 v 1 6

747.

( 10 z ) 1 6 ( 10 z ) 1 6

749.

2

751.

1 5 1 5

753.

1 6 1 6

755.

n 8 5 n 8 5

757.

32,768

759.

1 59,049 1 59,049

761.

x 8 x 8

763.

2 s 9 16 2 s 9 16

765.

z 2 z 2

Practice Test

767.

13 m 2 | n | 13 m 2 | n |

769.

4 13 + 5 2 4 13 + 5 2

771.

60 y 2 3 60 y 2 3

773.

1 4 q + 4 q 1 4 q + 4 q

775.

3x33x3 2y32y3

777.

y 2 y 2

779.

0 0

781.

343

783.

1 w 1 w

785.

6 4 6 4

787.

42

789.

6.1 seconds

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