12.4.10: Chapter 10

Be Prepared

10.1

$11x$

10.2

$3n+9$

10.3

$100$

10.4

$\frac{9}{16}$

10.5

$-8$

10.6

$2x+6$

10.7

$-44+33a$

10.8

$x^2+16x+63$

10.9

$\frac{1}{3}$

10.10

$32m^{15}$

10.11

$\frac{x}{y}$

10.12

ten thousand

10.13

twelve ten-thousandths

10.14

$8$

10.15

$2\cdot 2\cdot 2\cdot 7$

10.16

$-18a-33$

10.17

$4x^4+12x^3-4x^2$

Try It

10.1

1. ⓐ monomial
2. ⓑ polynomial
3. ⓒ trinomial
4. ⓓ binomial
5. ⓔ monomial

10.2

1. ⓐ binomial
2. ⓑ trinomial
3. ⓒ polynomial
4. ⓓ monomial
5. ⓒ monomial

10.3

1. ⓐ 1
2. ⓑ 1
3. ⓒ 4
4. ⓓ 2
5. ⓔ 0

10.4

1. ⓐ 0
2. ⓑ 2
3. ⓒ 4
4. ⓓ 5
5. ⓔ 3

10.5

17x²

10.6

−3y²

10.7

14n

10.8

−2a³

10.9

−2x² + 3y²

10.10

−2a² + b²

10.11

4x² − 8x + 10

10.12

11y² + 9y − 5

10.13

3y² + 3y + 3

10.14

3u² − u + 2

10.15

4n² + 12n

10.16

5a² + 8a + 8

10.17

1. ⓐ 13
2. ⓑ 3

10.18

1. ⓐ 114
2. ⓑ −2

10.19

4 feet

10.20

20 feet

10.21

1. ⓐ 64
2. ⓑ 11

10.22

1. ⓐ 81
2. ⓐ 21

10.23

1. ⓐ $\frac{25}{64}$
2. ⓑ $0.4489$

10.24

1. ⓐ $\frac{8}{125}$
2. ⓑ $0.016129$

10.25

1. ⓐ 16
2. ⓑ −16

10.26

1. ⓐ 64
2. ⓑ −64

10.27

x ¹⁵

10.28

x ¹⁶

10.29

p ¹⁰

10.30

m ⁸

10.31

6¹⁰

10.32

9¹⁵

10.33

y ⁴³

10.34

z ³⁹

10.35

x ²¹

10.36

y ¹⁵

10.37

1. ⓐ x ²⁸
2. ⓑ 7³²

10.38

1. ⓐ x ⁵⁴
2. ⓑ 8⁴²

10.39

196x²

10.40

144a²

10.41

256x⁴y⁴

10.42

216x³y³

10.43

x ⁴⁰

10.44

y ⁴²

10.45

−512x¹²y²¹

10.46

81a²⁰b²⁴

10.47

98n¹⁴

10.48

48m⁵

10.49

64u¹⁸v²²

10.50

675x⁷y¹⁸

10.51

−56x¹¹

10.52

54y⁹

10.53

12m⁵n⁶

10.54

12p¹¹q⁸

10.55

6x + 48

10.56

2y + 24

10.57

y² − 9y

10.58

p² − 13p

10.59

8x² + 24xy

10.60

18r² + 3rs

10.61

−32y³ − 20y² + 36y

10.62

−54x³ − 6x² + 6x

10.63

12x⁴ − 9x³ + 27x²

10.64

24y⁴ − 16y³ − 32y²

10.65

xp + 8p

10.66

ap + 4p

10.67

x² + 17x + 72

10.68

a² + 9a + 20

10.69

20x² + 51x + 27

10.70

80m² + 142m + 63

10.71

56y² − 13y − 3

10.72

15x² − 14x − 16

10.73

x² − xy + 5x − 5y

10.74

x² − x + 2xy − 2y

10.75

x² + 15x + 56

10.76

y² + 16y + 28

10.77

y² + 5y − 24

10.78

q² + q − 20

10.79

20a² + 37a − 18

10.80

49x² − 28x − 32

10.81

12x² − 60x − xy + 5y

10.82

12a² − 54a − 2ab + 9b

10.83

12m² − 55m + 63

10.84

42n² − 47n + 10

10.85

y³ − 8y² + 9y − 2

10.86

3x³ + 2x² − 3x + 10

10.87

y³ − 8y² + 9y − 2

10.88

3x³ + 2x² − 3x + 10

10.89

1. ⓐ x³
2. ⓑ 7⁹

10.90

1. ⓐ y ⁶
2. ⓑ 8⁸

10.91

1. ⓐ $\frac{1}{x^7}$
2. ⓑ $\frac{1}{{12}^{10}}$

10.92

1. ⓐ $\frac{1}{m^9}$
2. ⓑ $\frac{1}{7^6}$

10.93

1. ⓐ $b^8$
2. ⓑ $\frac{1}{z^6}$

10.94

1. ⓐ $\frac{1}{p^8}$
2. ⓑ $w^4$

10.95

1. ⓐ 1
2. ⓑ 1

10.96

1. ⓐ 1
2. ⓑ 1

10.97

1

10.98

1

10.99

1. ⓐ 1
2. ⓑ 7x²

10.100

1. ⓐ −23x²
2. ⓑ 1

10.101

1. ⓐ $\frac{49}{81}$
2. ⓑ $\frac{y^3}{512}$
3. ⓒ $\frac{p^6}{q^6}$

10.102

1. ⓐ $\frac{1}{64}$
2. ⓑ $-\frac{125}{m^3}$
3. ⓒ $\frac{r^4}{s^4}$

10.103

a ¹¹

10.104

b ¹⁹

10.105

k ²

10.106

$\frac{1}{d}$

10.107

f ¹²

10.108

$\frac{1}{b^{10}}$

10.109

$\frac{m^{15}}{n^{40}}$

10.110

$\frac{t^{20}}{u^{14}}$

10.111

$\frac{25b^2}{81c^6}$

10.112

$\frac{64p^{12}}{343q^{15}}$

10.113

$\frac{1}{y^{11}}$

10.114

9x⁵

10.115

7x⁴

10.116

16y³

10.117

$-\frac{12y}{x^2}$

10.118

$\frac{9}{a^5}$

10.119

$\frac{2a^6}{3b^2}$

10.120

$-\frac{3q^6}{5p^8}$

10.121

$\frac{4y^2}{7x^4}$

10.122

$\frac{5}{8m^5{n}^3}$

10.123

2xy²

10.124

−4ab⁵

10.125

1. ⓐ $\frac{1}{8}$
2. ⓑ $\frac{1}{100}$

10.126

1. ⓐ $\frac{1}{9}$
2. ⓑ $\frac{1}{\mathrm{10,000}}$

10.127

1. ⓐ $\frac{1}{25}$
2. ⓑ $-\frac{1}{25}$

10.128

1. ⓐ $\frac{1}{4}$
2. ⓑ $-\frac{1}{4}$

10.129

1. ⓐ $2$
2. ⓑ $\frac{1}{18}$

10.130

1. ⓐ $2$
2. ⓑ $\frac{1}{256}$

10.131

$\frac{1}{y^7}$

10.132

$\frac{1}{z^8}$

10.133

1. ⓐ $\frac{8}{p}$
2. ⓑ $\frac{1}{8p}$
3. ⓒ $-\frac{1}{8p}$

10.134

1. ⓐ $\frac{11}{q}$
2. ⓑ $\frac{1}{11q}$
3. ⓒ $-\frac{1}{11q}$

10.135

1. ⓐ $x^4$
2. ⓑ $\frac{1}{y^5}$
3. ⓒ $\frac{1}{z^9}$

10.136

1. ⓐ $a^5$
2. ⓑ $\frac{1}{b^4}$
3. ⓒ $\frac{1}{c^{15}}$

10.137

$\frac{1}{p^3{q}^3}$

10.138

$\frac{1}{r^2{s}^8}$

10.139

$-\frac{12v^5}{u}$

10.140

$\frac{30d^3}{c^8}$

10.141

$\frac{1}{x^4}$

10.142

$\frac{1}{y^4}$

10.143

$\frac{64}{a^8}$

10.144

$\frac{8}{c^{12}}$

10.145

x ¹¹

10.146

y ¹³

10.147

9.6 × 10⁴

10.148

4.83 × 10⁴

10.149

7.8 × 10⁻³

10.150

1.29 × 10⁻²

10.151

1,300

10.152

92,500

10.153

0.00012

10.154

0.075

10.155

0.06

10.156

0.009

10.157

400,000

10.158

20,000

10.159

18

10.160

16

10.161

7

10.162

11

10.163

8x²

10.164

9y³

10.165

3x

10.166

5m²

10.167

4(x + 3)

10.168

6(a + 4)

10.169

9(a + 1)

10.170

11(x + 1)

10.171

11(x − 4)

10.172

13(y − 4)

10.173

4(y² + 2y + 3)

10.174

6(x² + 7x − 2)

10.175

x(9x + 7)

10.176

a(5a − 12)

10.177

2x²(x + 6)

10.178

3y²(2y − 5)

10.179

9y(2y + 7)

10.180

8k(4k + 7)

10.181

6y(3y² − y − 4)

10.182

4x(4x² + 2x − 3)

10.183

−5(y + 7)

10.184

−8(2z + 7)

10.185

−7a(a − 3)

10.186

−x(6x − 1)

Section 10.1 Exercises

1.

binomial

3.

trinomial

5.

polynomial

7.

monomial

9.

5

11.

1

13.

0

15.

15x²

17.

−8u

19.

5a + 7b

21.

−4a −3b

23.

16x

25.

−17x⁶

27.

12y² + 4y + 8

29.

−3x² + 17x − 1

31.

4a² − 7a − 11

33.

4m² − 10m + 2

35.

11z + 8

37.

12s² − 16s + 9

39.

2p³ + p² + 9p + 10

41.

x² + 3x + 4

43.

11w − 66

45.

1. ⓐ 187
2. ⓑ 40
3. ⓒ 2

47.

1. ⓐ −104
2. ⓑ 4
3. ⓒ 40

49.

19 feet

51.

10 mpg

53.

Answers will vary.

Section 10.2 Exercises

55.

1,024

57.

$\frac{1}{4}$

59.

0.008

61.

625

63.

−625

65.

−10,000

67.

$-\frac{8}{27}$

69.

−0.25

71.

x ⁹

73.

a ⁵

75.

3¹⁴

77.

z ⁶

79.

x ^a+2

81.

y ^a+b

83.

u ⁸

85.

y ²⁰

87.

10¹²

89.

x ⁹⁰

91.

x ^2y

93.

5^xy

95.

25a²

97.

−216m³

99.

16r²s²

101.

256x⁴y⁴z⁴

103.

x ¹⁴

105.

a ³⁶

107.

45x³

109.

200a⁵

111.

8m¹⁸

113.

1,000x⁶y³

115.

16a¹²b⁸

117.

$\frac{8}{27}{x}^6{y}^3$

119.

1,024a¹⁰

121.

25,000p²⁴

123.

x ¹⁸ y ¹⁸

125.

144m⁸n²²

127.

−60x⁶

129.

72u⁷

131.

4r¹¹

133.

36a⁵b⁷

135.

8x²y⁵

137.

$\frac{1}{2}{x}^3{y}^3$

139.

1,679,616

141.

Answers will vary.

143.

Answers will vary.

Section 10.3 Exercises

145.

4x + 40

147.

15r − 360

149.

−3m − 33

151.

−8z + 40

153.

u² + 5u

155.

n³ − 3n²

157.

12x² − 120x

159.

−27a² − 45a

161.

24x² + 6xy

163.

55p² − 25pq

165.

3v² + 30v + 75

167.

8n³ − 8n² + 2n

169.

−8y³ − 16y² + 120y

171.

5q⁵ − 10q⁴ + 30q³

173.

−12z⁴ − 48z³ + 4z²

175.

2y² − 9y

177.

8w − 48

179.

x² + 10x + 24

181.

n² + 9n − 36

183.

y² + 11y + 24

185.

a² + 22a + 96

187.

u² − 14u + 45

189.

z² − 32z + 220

191.

x² + 3x − 28

193.

v² + 7v − 60

195.

6n² + 11n + 5

197.

20m² − 88m − 9

199.

16c² − 1

201.

15u² − 82u + 112

203.

2a² + 5ab + 3b²

205.

5x² − 20x − xy + 4y

207.

u³ + 7u² + 14u + 8

209.

3a³ + 31a² + 5a − 50

211.

y³ − 16y² + 69y − 54

213.

2x³ − 9x² − 17x − 6

215.

1. ⓐ 195
2. ⓑ 195
3. ⓒ Answers will vary.

217.

Answers will vary.

Section 10.4 Exercises

219.

4⁶

221.

x ⁹

223.

r ⁴

225.

$\frac{1}{y^{16}}$

227.

$\frac{1}{{10}^{12}}$

229.

$\frac{1}{a^8}$

231.

1

233.

1

235.

−1

237.

1. ⓐ 1
2. ⓑ 10

239.

1. ⓐ 1
2. ⓑ −27x⁵

241.

1. ⓐ 1
2. ⓑ 15

243.

7

245.

$\frac{243}{32}$

247.

$\frac{m^3}{216}$

249.

$\frac{x^{10}}{y^{10}}$

251.

$\frac{a^2}{9b^2}$

253.

x ³

255.

u ²

257.

$\frac{1}{y^2}$

259.

1

261.

$\frac{1}{x^{18}}$

263.

a ¹⁴

265.

y ³

267.

$\frac{1}{x^{10}}$

269.

$\frac{16r^{12}}{625s^4}$

271.

1

273.

$\frac{1}{r^3}$

275.

3x⁸

277.

8b⁶

279.

$\frac{\mathrm{-18}}{x^6}$

281.

2x

283.

$\frac{5}{6x^6}$

285.

$\frac{6r^2}{s^8}$

287.

$\frac{n^6}{8}$

289.

$-\frac{4y^6}{5x^2}$

291.

$\frac{4z}{3x^2{y}^3}$

293.

$\frac{10n^2}{m^4}$

295.

5u⁴v³

297.

1. ⓐ$18n^{10}$
2. ⓑ$12n^{10}$
3. ⓒ$45n^{20}$
4. ⓓ $5$

299.

1. ⓐ$q^8$
2. ⓑ $q^{15}$

301.

1. ⓐ $z$
2. ⓑ $\frac{1}{z}$

303.

$6y^6$

305.

$15c^6$

307.

$3x^2$

309.

$-y{z}^2$

311.

1,000,000

313.

Answers will vary.

315.

Answers will vary.

Section 10.5 Exercises

317.

$\frac{1}{64}$

319.

$\frac{1}{32}$

321.

$\frac{1}{10}$

323.

$\frac{4}{9}$

325.

$\frac{3}{5}$

327.

$\frac{3}{4}$

329.

1. ⓐ $\frac{1}{64}$
2. ⓑ $-\frac{1}{64}$

331.

1. ⓐ $\frac{1}{4096}$
2. ⓑ $-\frac{1}{4096}$

333.

1. ⓐ $\frac{10}{3}$
2. ⓑ $\frac{1}{30}$

335.

1. ⓐ $\frac{3}{25}$
2. ⓑ $\frac{1}{225}$

337.

$\frac{1}{p^3}$

339.

$\frac{1}{m^5}$

341.

1. ⓐ $\frac{3}{q}$
2. ⓑ $\frac{1}{3q}$
3. ⓒ $-\frac{1}{3q}$

343.

1. ⓐ $\frac{10}{k}$
2. ⓑ $\frac{1}{10k}$
3. ⓒ $-\frac{1}{10k}$

345.

r ³

347.

$\frac{1}{q^5}$

349.

$\frac{1}{z^8}$

351.

$\frac{1}{m}$

353.

$\frac{1}{x}$

355.

$\frac{u^2}{v^2}$

357.

$\frac{1}{a^2{b}^4}$

359.

$\frac{1}{p^5{q}^7}$

361.

$-\frac{21q^5}{p^3}$

363.

$\frac{32}{a^{3}b}$

365.

$\frac{1}{q^{100}}$

367.

$\frac{1}{x^4}$

369.

$\frac{1}{p^6}$

371.

m ⁶

373.

$\frac{9}{q^{10}}$

375.

$\frac{n^{18}}{64}$

377.

b ⁸

379.

m ⁷

381.

$\frac{1}{r^3}$

383.

p ³

385.

2.8 × 10⁵

387.

1.29 × 10⁶

389.

4.1 × 10⁻²

391.

1.03 × 10⁻⁵

393.

6.85 × 10⁹

395.

5.7 × 10⁻⁹

397.

830

399.

16,000,000,000

401.

0.028

403.

0.0000000615

405.

$15,000,000,000,000

407.

0.00001

409.

0.003

411.

0.00000735

413.

20,000,000

415.

50,000,000

417.

1. ⓐ 1.25 × 10⁻⁴
2. ⓐ 8,000

419.

11,441,304,000

421.

Answers will vary.

Section 10.6 Exercises

423.

15

425.

25

427.

4

429.

5

431.

3x

433.

12p³

435.

2a

437.

10y

439.

5x³

441.

7b²

443.

5(y + 3)

445.

4(b − 5)

447.

7(x − 1)

449.

3(n² + 7n + 4)

451.

6(q² + 5q + 7)

453.

c(9c + 22)

455.

x(17x + 7)

457.

q(4q + 7)

459.

3r(r + 9)

461.

10u(3u − 1)

463.

b(a + 8)

465.

11y(5 − y³)

467.

15c²(3c − 1)

469.

6c(c² − d²)

471.

24x²(2x + 3)

473.

18a³(8a³ + 5)

475.

10(y² + 5y + 4)

477.

12(u² − 3u − 9)

479.

5p²(p² − 4p − 3)

481.

8c³(c² + 5c − 7)

483.

−7(p + 12)

485.

−6b(3b + 11)

487.

−8a²(a − 4)

489.

−9b³(b² − 7)

491.

−4(4t² − 20t − 1)

493.

Answers will vary.

Review Exercises

494.

trinomial

496.

binomial

498.

2

500.

0

502.

15p

504.

−3n⁵

506.

10a² + 4a − 1

508.

6y² − 3y + 3

510.

8q³ + q² + 6q − 29

512.

995

514.

2,955

516.

−163

518.

64 feet

520.

216

522.

0.25

524.

p ¹³

526.

a ⁶

528.

y ¹²

530.

3¹⁰

532.

64n²

534.

256a⁸b⁸

536.

27a¹⁵

538.

x ²¹

540.

−54p⁵

542.

56x³y¹¹

544.

70 − 7x

546.

−625y⁴ + 5y

548.

a² + 7a + 10

550.

6x² − 19x − 7

552.

n² + 9n + 8

554.

5u² + 37u − 24

556.

p² + 11p + 28

558.

27c² − 3c − 4

560.

x³ − 2x² − 24x − 21

562.

m³ − m² − 72m − 180

564.

2⁶ or 64

566.

$\frac{1}{n^9}$

568.

1

570.

1

572.

$\frac{9}{25}$

574.

$\frac{125m^3}{n^3}$

576.

a ²

578.

$\frac{1}{x^{40}}$

580.

$\frac{1}{n}$

582.

9p⁹

584.

$-\frac{3}{y^4}$

586.

$\frac{4a^5}{b^2}$

588.

$\frac{4m^9}{n^4}$

590.

$\frac{1}{36}$

592.

$\frac{5}{16}$

594.

x ⁶

596.

$\frac{1}{u^3{v}^5}$

598.

k ⁶

600.

b ¹⁰

602.

5.3 × 10⁶

604.

9.7 × 10⁻² millimeter

606.

29,000

608.

0.375

610.

6,000

612.

30,000,000,000

614.

5

616.

4x²

618.

8(2u − 3)

620.

6p(p + 1)

622.

−9a³(a² + 1)

624.

5(y² − 11y + 9)

Practice Test

626.

1. ⓐ trinomial
2. ⓑ 4

628.

6x² − 3x + 11

630.

n ⁵

632.

−48x⁵y⁹

634.

s² + 17s + 72

636.

55a² − 41a + 6

638.

24a² + 34ab − 45b²

640.

x ¹⁴

642.

$\frac{4r}{s^6}$

644.

3y² − 7x

646.

$\frac{1}{8y^3}$

648.

x ⁹

650.

−6x(x + 5)

652.

0.000525

654.

$\mathrm{300,000}$