Intermediate Algebra 2e

# Chapter 8

## Be Prepared

8.1

8; −1; -729

8.2

3.85

8.3

$x6x6$; $y6y6$; $z12z12$

8.4

$x 5 x 5$

8.5

$1 y 8 1 y 8$

8.6

$n 12 n 12$

8.7

$53 60 53 60$

8.8

$64 x 6 y 15 64 x 6 y 15$

8.9

$1 125 1 125$

8.10

$2 x 2 + 11 x − 8 2 x 2 + 11 x − 8$

8.11

$8 + 2 a − a 2 8 + 2 a − a 2$

8.12

$81 − 90 y + 25 y 2 81 − 90 y + 25 y 2$

8.13

$5 8 5 8$

8.14

$x 6 x 6$

8.15

$49 − 9 x 2 49 − 9 x 2$

8.16

$y 2 − 6 y + 9 y 2 − 6 y + 9$

8.17

$x = 5 2 x = 5 2$

8.18

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

8.19

$( − ∞ , 1 2 ] ( − ∞ , 1 2 ]$

8.20

$f ( 2 ) = 2 , f ( −1 ) = −7 , f ( 0 ) = −4 f ( 2 ) = 2 , f ( −1 ) = −7 , f ( 0 ) = −4$

8.21

$domain: [ 0 , ∞ ) ; range: [ 0 , ∞ ) domain: [ 0 , ∞ ) ; range: [ 0 , ∞ )$

8.22

$−4,0.5–,73,3,81;−4,0.5–,73,3,81;$ $7;7;$ $−4,−7,0.5–,73,3,81−4,−7,0.5–,73,3,81$

8.23

$2 x 2 − x − 15 2 x 2 − x − 15$

8.24

$5 + 15 2 5 + 15 2$

## Try It

8.1

$−8−8$ 15

8.2

10 $−11−11$

8.3

not a real number $−9−9$

8.4

$−7−7$ not a real number

8.5

3 4 3

8.6

10 2 4

8.7

$−3−3$ not real $−2−2$

8.8

$−6−6$ not real $−4−4$

8.9

$6<38<76<38<7$
$4<933<54<933<5$

8.10

$9<84<109<84<10$
$5<1523<65<1523<6$

8.11

$≈3.32≈3.32$ $≈4.14≈4.14$
$≈3.36≈3.36$

8.12

$≈3.61≈3.61$ $≈4.38≈4.38$
$≈3.15≈3.15$

8.13

$|b||b|$ w $|m||m|$ q

8.14

$|y||y|$ p $|z||z|$ q

8.15

$|y9||y9|$ $z6z6$

8.16

$m2m2$ $|b5||b5|$

8.17

$|u3||u3|$ $v5v5$

8.18

$c4c4$ $d4d4$

8.19

$8|x|8|x|$ $−10|p|−10|p|$

8.20

$13|y|13|y|$ $−11|y|−11|y|$

8.21

$3x93x9$ $3|q7|3|q7|$

8.22

$5q35q3$ $3q53q5$

8.23

$10|ab|10|ab|$ $12p6q1012p6q10$
$2x10y42x10y4$

8.24

$15|mn|15|mn|$ $13|x5y7|13|x5y7|$
$3w12z53w12z5$

8.25

$4 3 4 3$

8.26

$3 5 3 5$

8.27

$122122$ $333333$ $244244$

8.28

$123123$ $553553$ $394394$

8.29

$b2bb2b$ $|y|y24|y|y24$ $zz23zz23$

8.30

$p4pp4p$ $yy35yy35$
$q2q6q2q6$

8.31

$4y22y4y22y$ $3p32p33p32p3$
$2q24q242q24q24$

8.32

$5a43a5a43a$ $4m32m234m32m23$
$3|n|2n343|n|2n34$

8.33

$7|a3|b22ab7|a3|b22ab$
$2xy7x2y32xy7x2y3$ $2|x|y22x42|x|y22x4$

8.34

$6m4|n5|5mn6m4|n5|5mn$
$2x2y9y232x2y9y23$ $2|xy|5x342|xy|5x34$

8.35

$−4−4$ $no real numberno real number$

8.36

$−553−553$ no real number

8.37

$5+535+53$ $2−32−3$

8.38

$2+722+72$ $2−52−5$

8.39

$5454$ $3535$ $2323$

8.40

$7979$ $2525$ $1313$

8.41

$|a||a|$ $|x||x|$ $y3y3$

8.42

$x2x2$ $m2m2$ $n2n2$

8.43

$2 | p | 6 p 7 2 | p | 6 p 7$

8.44

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

8.45

$4|m|5m|n3|4|m|5m|n3|$ $3c34c3d23c34c3d2$
$2x25x24|y|2x25x24|y|$

8.46

$3u36uv43u36uv4$ $2r53s22r53s2$
$3|m3|2m24|n3|3|m3|2m24|n3|$

8.47

$5|y|x65|y|x6$ $2xyy2332xyy233$
$|ab|a42|ab|a42$

8.48

$2|m|35|n3|2|m|35|n3|$ $3xyx2353xyx235$
$2|ab|a2432|ab|a243$

8.49

$7z27z2$ $−523−523$
$3|m|2m243|m|2m24$

8.50

$8m48m4$ $−4−4$ $3|n|243|n|24$

8.51

$tt$ $m3m3$ $r4r4$

8.52

$b6b6$ $z5z5$ $p4p4$

8.53

$(10m)12(10m)12$ $(3n)15(3n)15$
$3(6y)143(6y)14$

8.54

$(3k)17(3k)17$ $(5j)14(5j)14$
$8(2a)138(2a)13$

8.55

6 2 2

8.56

10 3 3

8.57

No real solution $−8−8$
$1818$

8.58

No real solution $−4−4$
$1414$

8.59

$x52x52$ $(3y)34(3y)34$ $(2m3n)52(2m3n)52$

8.60

$a25a25$ $(5ab)53(5ab)53$
$(7xyz)32(7xyz)32$

8.61

9 $17291729$ $1818$

8.62

8 $1919$ $11251125$

8.63

$−64−64$ $−164−164$ not a real number

8.64

$−729−729$ $−1729−1729$ not a real number

8.65

$x32x32$ $x8x8$ $1x1x$

8.66

$y118y118$ $m2m2$ $1d1d$

8.67

$8x158x15$ $x12y13x12y13$

8.68

$729n35729n35$ $a2b23a2b23$

8.69

$m2m2$ $5nm145nm14$

8.70

$u3u3$ $3x15y133x15y13$

8.71

$−2−2$ $11x311x3$
$3x4−5y43x4−5y4$

8.72

$−43−43$ $8y38y3$
$5m4−2m35m4−2m3$

8.73

$−27x−27x$ $−5xy4−5xy4$

8.74

$−3y−3y$ $37mn337mn3$

8.75

$9292$ $223223$ $3333$

8.76

$7373$ $−1053−1053$ $−323−323$

8.77

$−m32m−m32m$ $x25x3x25x3$

8.78

$−p3p−p3p$
$4y4y23−2y4n234y4y23−2y4n23$

8.79

$12151215$ $−1843−1843$

8.80

$272272$ $−3623−3623$

8.81

$288x35288x35$ $8y6y248y6y24$

8.82

$144y25y144y25y$ $−36a3a4−36a3a4$

8.83

$18+618+6$ $−243−233−243−233$

8.84

$−40+42−40+42$ $−3−183−3−183$

8.85

$−66+157−66+157$
$x23−5x3+6x23−5x3+6$

8.86

$41−141141−1411$
$x23+4x3+3x23+4x3+3$

8.87

$1 + 9 21 1 + 9 21$

8.88

$−12 − 20 3 −12 − 20 3$

8.89

$102+202102+202$ $55+6655+66$

8.90

$41−12541−125$
$121−3610121−3610$

8.91

$−11 −11$

8.92

$−159 −159$

8.93

$5s85s8$ $2a2a$

8.94

$5q265q26$ $2b2b$

8.95

$9x2y29x2y2$ $−4xy−4xy$

8.96

$10n3m10n3m$ $−3pq2−3pq2$

8.97

$4 x y 2 x 4 x y 2 x$

8.98

$4 a b 3 b 4 a b 3 b$

8.99

$533533$ $6868$ $2xx2xx$

8.100

$655655$ $146146$ $5xx5xx$

8.101

$49374937$ $90369036$ $53y233y53y233y$

8.102

$432432$ $150310150310$ $25n235n25n235n$

8.103

$27432743$ $12441244$ $35x345x35x345x$

8.104

$1254512545$ $14441444$
$24x34x24x34x$

8.105

$− 3 ( 1 + 5 ) 4 − 3 ( 1 + 5 ) 4$

8.106

$4 + 6 5 4 + 6 5$

8.107

$5 ( x − 2 ) x − 2 5 ( x − 2 ) x − 2$

8.108

$10 ( y + 3 ) y − 3 10 ( y + 3 ) y − 3$

8.109

$( p + 2 ) p − 2 2 ( p + 2 ) p − 2 2$

8.110

$( q − 10 ) q − 10 2 ( q − 10 ) q − 10 2$

8.111

$m = 23 3 m = 23 3$

8.112

$z = 3 10 z = 3 10$

8.113

$no solution no solution$

8.114

$no solution no solution$

8.115

$x = 2 , x = 3 x = 2 , x = 3$

8.116

$y = 5 , y = 6 y = 5 , y = 6$

8.117

$x = −6 x = −6$

8.118

$x = −9 x = −9$

8.119

$x = 8 x = 8$

8.120

$x = 6 x = 6$

8.121

$m = 7 m = 7$

8.122

$n = 3 n = 3$

8.123

$a = 63 a = 63$

8.124

$b = 311 b = 311$

8.125

$x = 3 x = 3$

8.126

$x = − 6 5 x = − 6 5$

8.127

$x = 4 x = 4$

8.128

$x = 9 x = 9$

8.129

$x = 5 x = 5$

8.130

$x = 0 x = 4 x = 0 x = 4$

8.131

9 seconds

8.132

$3.53.5$ seconds

8.133

$42.742.7$ feet

8.134

$54.154.1$ feet

8.135

$f(6)=4f(6)=4$ no value at $x=0x=0$

8.136

$g(4)=5g(4)=5$ no value at $f(−3)f(−3)$

8.137

$g(4)=2g(4)=2$ $g(1)=−1g(1)=−1$

8.138

$h(2)=2h(2)=2$
$h(−5)=−3h(−5)=−3$

8.139

$f(4)=2f(4)=2$ $f(−1)=1f(−1)=1$

8.140

$g(16)=3g(16)=3$ $g(3)=2g(3)=2$

8.141

$[ 5 6 , ∞ ) [ 5 6 , ∞ )$

8.142

$( − ∞ , 4 5 ] ( − ∞ , 4 5 ]$

8.143

$( −3 , ∞ ) ( −3 , ∞ )$

8.144

$( 5 , ∞ ) ( 5 , ∞ )$

8.145

$( − ∞ , ∞ ) ( − ∞ , ∞ )$

8.146

$( − ∞ , ∞ ) ( − ∞ , ∞ )$

8.147

domain: $[−2,∞)[−2,∞)$

range: $[0,∞)[0,∞)$

8.148

domain: $[2,∞)[2,∞)$

range: $[0,∞)[0,∞)$

8.149

domain: $(−∞,∞)(−∞,∞)$

range: $(−∞,∞)(−∞,∞)$

8.150

domain: $(−∞,∞)(−∞,∞)$

range: $(−∞,∞)(−∞,∞)$

8.151

$9i9i$ $5i5i$ $32i32i$

8.152

$6i6i$ $3i3i$ $33i33i$

8.153

$6 2 i 6 2 i$

8.154

$7 3 i 7 3 i$

8.155

$6+5i6+5i$ $6−3i6−3i$

8.156

$−2−6i−2−6i$ $2+9i2+9i$

8.157

$12 + 20 i 12 + 20 i$

8.158

$12 − 6 i 12 − 6 i$

8.159

$−11 − 7 i −11 − 7 i$

8.160

$−5 − 10 i −5 − 10 i$

8.161

$−21 + 21 i −21 + 21 i$

8.162

$9 − 40 i 9 − 40 i$

8.163

$−14 −14$

8.164

$−54 −54$

8.165

$−12 − 22 3 i −12 − 22 3 i$

8.166

$6 + 12 2 i 6 + 12 2 i$

8.167

25

8.168

29

8.169

109

8.170

41

8.173

$4 17 + 16 17 i 4 17 + 16 17 i$

8.174

$2 5 + 4 5 i 2 5 + 4 5 i$

8.175

$3 2 − 3 2 i 3 2 − 3 2 i$

8.176

$4 5 − 2 5 i 4 5 − 2 5 i$

8.177

$− i − i$

8.178

$1 1$

## Section 8.1 Exercises

1.

8 $−9−9$

3.

14 $−1−1$

5.

$2323$ $−0.1−0.1$

7.

not real number $−17−17$

9.

$−15−15$ not real number

11.

6 4

13.

8 3 1

15.

$−2−2$ $not realnot real$ $−2−2$

17.

$−5−5$ $not realnot real$ $−4−4$

19.

$8<70<98<70<9$
$4<713<54<713<5$

21.

$14<200<1514<200<15$
$5<1373<65<1373<6$

23.

$≈4.36≈4.36$ $≈4.46≈4.46$
$≈3.14≈3.14$

25.

$≈7.28≈7.28$ $≈5.28≈5.28$
$≈4.61≈4.61$

27.

u $|v||v|$

29.

$|y||y|$ $mm$

31.

$|x3||x3|$ $y8y8$

33.

$x12x12$ $|y11||y11|$

35.

$x3x3$ $|y3||y3|$

37.

$m2m2$ $n4n4$

39.

$7|x|7|x|$ $−9|x9|−9|x9|$

41.

$11m1011m10$ $−8|a|−8|a|$

43.

$2x22x2$ $2y22y2$

45.

$6a26a2$ $2b42b4$

47.

$12|xy|12|xy|$ $13w4|y5|13w4|y5|$
$2a17b22a17b2$

49.

$11|ab|11|ab|$ $3c4d63c4d6$
$4x5y224x5y22$

51.

53.

## Section 8.2 Exercises

55.

$3 3 3 3$

57.

$5 5 5 5$

59.

$7 3 7 3$

61.

$20 2 20 2$

63.

$224224$ $225225$

65.

$244244$ $443443$

67.

$| y5 |y| y5 |y$ $rr23rr23$ $s2s24s2s24$

69.

$n10nn10n$ $q2q23q2q23$
$|n|n28|n|n28$

71.

$5r65r5r65r$ $3x4x233x4x23$
$2|y|3y242|y|3y24$

73.

$11|m11|2m11|m11|2m$ $3m25m243m25m24$ $2n5n352n5n35$

75.

$7|m3n5|3mn7|m3n5|3mn$ $2x2y26y32x2y26y3$ $2|xy|2x42|xy|2x4$

77.

$8|qr3|3qr8|qr3|3qr$ $3m3n32n33m3n32n3$ $3a2b2a43a2b2a4$

79.

$−643−643$ not real

81.

$−2−2$ not real

83.

$5+235+23$ $5−65−6$

85.

$1+351+35$ $1+101+10$

87.

$3434$ $2323$ $1313$

89.

$5353$ $3535$ $1414$

91.

$x2x2$ $p3p3$ $|q||q|$

93.

$1y21y2$ $u2u2$ $|v3||v3|$

95.

$4 | x 3 | 6 x 11 4 | x 3 | 6 x 11$

97.

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

99.

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

101.

$2 | q 3 | 7 15 2 | q 3 | 7 15$

103.

$5r43rs45r43rs4$ $3a22a23b3a22a23b$
$2|c|4c4|d|2|c|4c4|d|$

105.

$2|p3|7p|q|2|p3|7p|q|$ $3s23s23t3s23s23t$
$2|p3|4p34|q3|2|p3|4p34|q3|$

107.

$4|xy|34|xy|3$ $y2x32y2x32$ $|ab|a42|ab|a42$

109.

$12|pq|12|pq|$ $2cdd2352cdd235$
$|mn|2|mn|2$

111.

$3p4p|q|3p4p|q|$ $224224$
$2x2x52x2x5$

113.

$5|m3|5|m3|$ $553553$
$3|y|3y243|y|3y24$

115.

117.

## Section 8.3 Exercises

119.

$xx$ $y3y3$ $z4z4$

121.

$u5u5$ $v9v9$ $w20w20$

123.

$x17x17$ $y19y19$ $f15f15$

125.

$(7c)13(7c)13$ $(12d)17(12d)17$
$2(6b)142(6b)14$

127.

$(21p)12(21p)12$ $(8q)14(8q)14$
$4(36r)164(36r)16$

129.

9 5 8

131.

2 4 5

133.

$−6−6$ $−6−6$ $1616$

135.

not real $−3−3$ $1313$

137.

not real $−6−6$ $1616$

139.

not real $−10−10$ $110110$

141.

$m52m52$ $(3y)73(3y)73$ $(4x5y)35(4x5y)35$

143.

$u25u25$ $(6x)53(6x)53$ $(18a5b)74(18a5b)74$

145.

32,768 $17291729$ 9

147.

4 $1919$ not real

149.

$−27−27$ $−127−127$ not real

151.

$c78c78$ $p9p9$ $1r1r$

153.

$y54y54$ $x8x8$ $1m1m$

155.

$81q281q2$ $a12ba12b$

157.

$8u148u14$ $8p12q348p12q34$

159.

$r72r72$ $6st6st$

161.

$c2c2$ $2x3y2x3y$

163.

## Section 8.4 Exercises

165.

$3232$ $7m37m3$ $6m46m4$

167.

$9595$ $12a312a3$ $62z462z4$

169.

$42a42a$ 0

171.

$3c3c$ $4pq34pq3$

173.

$−23−23$ $−253−253$ $324324$

175.

$7373$ $723723$ $354354$

177.

$a22aa22a$ 0

179.

$2c35c2c35c$ $14r22r2414r22r24$

181.

$4 y 2 4 y 2$

183.

$−186−186$ $−6493−6493$

185.

$−302−302$ $624624$

187.

$72z2372z23$ $45x22345x223$

189.

$−42z52z−42z52z$ $−8y6y4−8y6y4$

191.

$14+5714+57$ $463+343463+343$

193.

$44−31144−311$ $324+544324+544$

195.

$60 + 2 3 60 + 2 3$

197.

$30+18230+182$ $x23−2x3−3x23−2x3−3$

199.

$−55+1310−55+1310$
$2x23+8x3+62x23+8x3+6$

201.

$23 + 3 30 23 + 3 30$

203.

$−439 − 2 77 −439 − 2 77$

205.

$14+6514+65$ $79−20379−203$

207.

$87−18687−186$
$163+607163+607$

209.

14

211.

$−227 −227$

213.

$19 19$

215.

$9 x 2 3 − 4 9 x 2 3 − 4$

217.

$5 3 5 3$

219.

$9 2 9 2$

221.

$− 5 4 − 5 4$

223.

$10c23−9c33 10 c 2 3 − 9 c 3 3$

225.

$2 3 2 3$

227.

$17 q 2 17 q 2$

229.

$3 7 3 7$

231.

$−42 9 3 −42 9 3$

233.

29

235.

$29 − 7 17 29 − 7 17$

237.

$54 − 36 2 54 − 36 2$

239.

$6 + 3 2 3 6 + 3 2 3$

241.

243.

## Section 8.5 Exercises

245.

$4343$ $4343$

247.

$10m2710m27$ $3y3y$

249.

$56r256r2$ $2x32x3$

251.

$6pq26pq2$ $−2a2b−2a2b$

253.

$8m43n48m43n4$ $−2x23y2−2x23y2$

255.

$2 x 2 7 y 2 x 2 7 y$

257.

$2 a b 2 a 3 2 a b 2 a 3$

259.

$563563$ $239239$ $25xx25xx$

261.

$677677$ $2101521015$ $43pp43pp$

263.

$25352535$ $45364536$ $26a233a26a233a$

265.

$121311121311$ $28362836$ $9x3x9x3x$

267.

$3434734347$ $40444044$ $24x24x24x24x$

269.

$943943$ $50445044$ $23a34a23a34a$

271.

$−2 ( 1 + 5 ) −2 ( 1 + 5 )$

273.

$3 ( 3 + 7 ) 3 ( 3 + 7 )$

275.

$3 ( m + 5 ) m − 5 3 ( m + 5 ) m − 5$

277.

$2 ( x + 6 ) x − 6 2 ( x + 6 ) x − 6$

279.

$( r + 5 ) r − 5 2 ( r + 5 ) r − 5 2$

281.

$( x + 2 2 ) x − 8 2 ( x + 2 2 ) x − 8 2$

283.

285.

## Section 8.6 Exercises

287.

$x = 14 x = 14$

289.

no solution

291.

$x = −4 x = −4$

293.

$m = 14 m = 14$

295.

$v = 17 v = 17$

297.

$m = 7 2 m = 7 2$

299.

no solution

301.

$u = 3 , u = 4 u = 3 , u = 4$

303.

$r = 1 , r = 2 r = 1 , r = 2$

305.

$x = 10 x = 10$

307.

$x = −8 x = −8$

309.

$x = 8 x = 8$

311.

$x = −4 x = −4$

313.

$x = 7 x = 7$

315.

$x = 3 x = 3$

317.

$z = 21 z = 21$

319.

$x = 42 x = 42$

321.

$r = 3 r = 3$

323.

$u = 3 u = 3$

325.

$r = −2 r = −2$

327.

$x = 1 x = 1$

329.

$x = −8 , x = 2 x = −8 , x = 2$

331.

$a = 0 a = 0$

333.

$u = 9 4 u = 9 4$

335.

$a = 4 a = 4$

337.

$x = 0 x = 4 x = 0 x = 4$

339.

$x = 1 x = 5 x = 1 x = 5$

341.

$x = 9 x = 9$

343.

$8.78.7$ feet

345.

$4.74.7$ seconds

347.

72 feet

349.

## Section 8.7 Exercises

351.

$f(5)=4f(5)=4$ no value at $x=0x=0$

353.

$g(4)=5g(4)=5$ $g(8)=7g(8)=7$

355.

$F(1)=1F(1)=1$ $F(−11)=5F(−11)=5$

357.

$G(5)=26G(5)=26$ $G(2)=3G(2)=3$

359.

$g(6)=2g(6)=2$ $g(−2)=−2g(−2)=−2$

361.

$h(−2)=0h(−2)=0$ $h(6)=243h(6)=243$

363.

$f(0)=0f(0)=0$ $f(2)=2f(2)=2$

365.

$g(1)=0g(1)=0$ $g(−3)=2g(−3)=2$

367.

$[ 1 3 , ∞ ) [ 1 3 , ∞ )$

369.

$( − ∞ , 2 3 ] ( − ∞ , 2 3 ]$

371.

$( 2 , ∞ ) ( 2 , ∞ )$

373.

$( − ∞ , −3 ] ∪ ( 2 , ∞ ) ( − ∞ , −3 ] ∪ ( 2 , ∞ )$

375.

$( − ∞ , ∞ ) ( − ∞ , ∞ )$

377.

$( − ∞ , ∞ ) ( − ∞ , ∞ )$

379.

$[ − 3 8 , ∞ ) [ − 3 8 , ∞ )$

381.

$( − ∞ , ∞ ) ( − ∞ , ∞ )$

383.

domain: $[−1,∞)[−1,∞)$

$[0,∞)[0,∞)$

385.

domain: $[−4,∞)[−4,∞)$

$[0,∞)[0,∞)$

387.

domain: $[0,∞)[0,∞)$

$[2,∞)[2,∞)$

389.

domain: $[0,∞)[0,∞)$

$[0,∞)[0,∞)$

391.

domain: $(−∞,3](−∞,3]$

$[0,∞)[0,∞)$

393.

domain: $[0,∞)[0,∞)$

$(−∞,0](−∞,0]$

395.

domain: $(−∞,∞)(−∞,∞)$

$(−∞,∞)(−∞,∞)$

397.

domain: $(−∞,∞)(−∞,∞)$

$(−∞,∞)(−∞,∞)$

399.

domain: $(−∞,∞)(−∞,∞)$

$(−∞,∞)(−∞,∞)$

401.

domain: $(−∞,∞)(−∞,∞)$

$(−∞,∞)(−∞,∞)$

403.

domain: $(−∞,∞)(−∞,∞)$

$(−∞,∞)(−∞,∞)$

405.

407.

## Section 8.8 Exercises

409.

$4i4i$ $11i11i$ $22i22i$

411.

$10i10i$ $13i13i$ $35i35i$

413.

$9 3 i 9 3 i$

415.

$8 2 i 8 2 i$

417.

$8 + 7 i 8 + 7 i$

419.

$14 + 2 i 14 + 2 i$

421.

$−2 + 2 i −2 + 2 i$

423.

$8 + 5 i 8 + 5 i$

425.

$7 − 13 i 7 − 13 i$

427.

$25 − 2 2 i 25 − 2 2 i$

429.

$12 + 20 i 12 + 20 i$

431.

$−12 + 18 i −12 + 18 i$

433.

$−38 + + 9 i −38 + + 9 i$

435.

$27 + 15 i 27 + 15 i$

437.

$−7 + 24 i −7 + 24 i$

439.

$−5 + 12 i −5 + 12 i$

441.

$−30 −30$

443.

$−30 −30$

445.

$−44 − 4 i 3 −44 − 4 i 3$

447.

$−20 − 2 2 i −20 − 2 2 i$

449.

5

451.

53

453.

50

455.

85

457.

i

459.

$2 25 + 11 25 i 2 25 + 11 25 i$

461.

$6 13 + 9 13 i 6 13 + 9 13 i$

463.

$− 12 13 − 8 13 i − 12 13 − 8 13 i$

465.

$4 3 − 1 3 i 4 3 − 1 3 i$

467.

$− 3 4 + 1 2 i − 3 4 + 1 2 i$

469.

i

471.

$−1 −1$

473.

1

475.

i

477.

479.

## Review Exercises

481.

15 $−4−4$

483.

2 3 3

485.

$8<68<98<68<9$
$4<843<54<843<5$

487.

a $bb$

489.

$m2m2$ $n4n4$

491.

$6a26a2$ $2b42b4$

493.

$5 5 5 5$

495.

$553553$ $226226$

497.

$4|s7|5s4|s7|5s$ $2a3a252a3a25$
$2|b|2b62|b|2b6$

499.

$−2−2$ not real

501.

$6767$ $2323$ $1212$

503.

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

505.

$12|pq|12|pq|$ $2cd5d232cd5d23$
$|mn|2|mn|2$

507.

$rr$ $s3s3$ $t4t4$

509.

5 3 2

511.

$−2−2$ $1313$ $−5−5$

513.

125 $127127$ 16

515.

$6363$ $b9b9$ $1w1w$

517.

$4242$ $9p39p3$ $2x32x3$

519.

$7373$ $723723$ $354354$

521.

$37 y 3 37 y 3$

523.

$126x2x126x2x$ $48a5a2348a5a23$

525.

$71−22771−227$
$x23−8x3+15x23−8x3+15$

527.

$27+81127+811$ $29−12529−125$

529.

$9 x 2 3 − 4 9 x 2 3 − 4$

531.

$8m43n48m43n4$ $−2x23y2−2x23y2$

533.

$121311121311$ $28362836$ $9x3x9x3x$

535.

$− 7 ( 2 + 6 ) 2 − 7 ( 2 + 6 ) 2$

537.

$( x + 2 2 ) x − 8 2 ( x + 2 2 ) x − 8 2$

539.

no solution

541.

$u = 3 , u = 4 u = 3 , u = 4$

543.

$x = −4 x = −4$

545.

$r = 3 r = 3$

547.

$x = −8 , x = 2 x = −8 , x = 2$

549.

$x = 3 x = 3$

551.

$64.864.8$ feet

553.

$G(5)=26G(5)=26$ $G(2)=3G(2)=3$

555.

$g(1)=0g(1)=0$ $g(−3)=2g(−3)=2$

557.

$( 2 , ∞ ) ( 2 , ∞ )$

559.

$− ∞ , 10 7 − ∞ , 10 7$

561.

domain: $[0,∞)[0,∞)$

range: $[0,∞)[0,∞)$

563.

domain: $(−∞,∞)(−∞,∞)$

range: $(−∞,∞)(−∞,∞)$

565.

$8 2 i 8 2 i$

567.

$8 + 5 i 8 + 5 i$

569.

$23 + 14 i 23 + 14 i$

571.

$−8 −8$

573.

$−5 + 12 i −5 + 12 i$

575.

$2 25 + 11 25 i 2 25 + 11 25 i$

577.

1

## Practice Test

579.

$5 x 3 5 x 3$

581.

$2 x 2 y 9 x 2 y 3 2 x 2 y 9 x 2 y 3$

583.

$1414$ $−343−343$

585.

$x 7 4 x 7 4$

587.

$− x 2 3 x − x 2 3 x$

589.

$36 x 4 2 36 x 4 2$

591.

$2 − 7 3 2 − 7 3$

593.

$7 x 2 x 3 | y 3 | y 7 x 2 x 3 | y 3 | y$

595.

$3 ( 2 − 3 ) 3 ( 2 − 3 )$

597.

$−12 + 8 i −12 + 8 i$

599.

$1 1$

601.

$x = 4 x = 4$

603.

domain: $[−2,∞)[−2,∞)$

range: $[0,∞)[0,∞)$