17.base: ; exponent: 5; 19.base: ; exponent: 4
21.base: x; exponent: 4 23. is a sum, not a product;
. 25. 27. 29. 31.
33. 35. 37. 39.The product rule does not
apply. 41.The product rule does not apply. 43. 45. 47.
49. 51. 53. 55. 57. 59. 61.
63. 65. 67. 69. 71. 73.
75. 77. 79. 81.
83.Using the product rule, it is simplified as follows:
. 85. 87. 89. 91. , ,
, ; One way is to choose a positive number greater than 1
and substitute it for ain each expression. Then arrange the terms from
least to greatest. 93.$304.16 95.$1843.88 97. 99.
101. 12 103. 3
Section 5.2 (pages 308–310)
- 1 3. 1 5. 7. 9. 0 11. 0 13. 0 15. 0 17. (a)B
(b)C (c)D (d)B (e)E (f )B 19. 2 21. 23. 16
- 1 60.
- ; This supports the definition of 0 as an exponent.
- 343 65. 67. 69. 71. 6 x 73.
- 85.The student
attempted to use the quotient rule with unequal bases. The correct way to
simplify is. 87.64,280 89. 1530
91.3.8 93.0.277
Summary Exercises on the Rules for
Exponents (page 311)
- 0 11. 12. 13.
- 6 ab 19. 20. 1
- 1 23. 24. 0 25. 26.
- 0 31. 32.
- 1 37. 38.
- (a)D (b)D (c)E (d)B (e)J(f)F (g)I
(h)B (i)E (j)F
- 1
- (a)D (b)D (c)E (d)B (e)J(f)F (g)I
18 p mn (^3) p 3
r (^10) q
(^14) t
2 s^2
7
5 p^10 q^924
9
x^6
343
x^15
x^6 y^6
q
8 p^6 r^3
x^15
216 z^9
1
a^8 b^12 c^16
27 y^18
4 x^8
343 a - 1
(^6) b 9
8
61
900
a^6
b^4
y^11
x^11
x^8
3
5 x^6
300 x^3
y^3
9
r^2 s^2 t^10
1
z^2
x^6
y^5
(^1130) y (^12) z 3
1
k^4 t^12
c^22
x^4 y^6
16
729 w^3 x^9
y^12
105 x^7 y^14 - 128 a^10 b^15 c^4
163
22
12423
22
=^2
12
22
= 210 = 1024
9 z^2
400 x^3
108
y^5 z^3
a^11
2 b^5
(^1) x (^3) y 9
xyz
1
m^10 n^5
x^2 z^4
y^2
64 x
9
1
(^7) x 2
(^3) , or
50 1 = 50
52
52
a+b 1 x+ 2 y 22
yz^2
4 x^3
r^9
p^5
q^8
52
43
, or
25
2 r 64
(^12552) , or 25 x (^1563) , or 216 4
9
53
32
3649 811 158 - 187 27 53 , or 125 , or
1
64
- 1 - 1
(^19) - 8
- 1 - a 231 - a 24
106 =1,000,000 12 x^56 p^7125 x^6 - a^4 - a^3
110223 = 102 #^3 =53 a^6 b^15
c^18
, or^125 a(^6) b 15
c^18
x^214 w^4 x^26 y^7 - r^18 s^17
(^9212) x (^12) - 65 p (^565) x (^10) y 15
5
83
55
25
x^3
23
a^3
b^3
1
23
98
58
55 x^5 y^5512 - 815 8 q^3 r^3
46 t^2073 r^3
- 56 r^742 p^10 - 30 x^9
52 + 53 = 25 + 125 = 150 58 412 1 - 729 t^24
52 + 53- 3 - 243 - 6 x Connections ( page 316) 1.The Indonesia earthquake was 10 times
as powerful as the Peru earthquake. 2.The Afghanistan earthquake had
one-hundredth the power of the China earthquake. 3.The Alaska
earthquake was about 19.95 times as powerful as the China earthquake.
4.“ ” corresponds to a factor of 1000 times stronger; “ ”
corresponds to a factor of one-tenth as strong.
Section 5.3 (pages 316–319)- (a)C (b)A (c)B (d)D 3.in scientific notation
5.not in scientific notation; 7.not in scientific notation;
9.not in scientific notation; 11.It is written as
the product of a power of 10 and a number whose absolute value is
between 1 and 10 (inclusive of 1). Some examples are and
. 13. 15. 17.
- 25.750,000
27.5,677,000,000,000 29.1,000,000,000,000 31.6.21
33.0.00078 35.0.000000005134 37. 39.
- 25.750,000
- (a) (b)600,000,000,000 43. (a)
(b)15,000,000 45. (a) (b) 60,000 - (a) (b) 240 49. (a) (b)0.063
- (a) (b)0.0003 53. (a) (b) 40
- (a) (b)0.000013 57. (a) (b) 500
- (a) (b) 61. (a)
(b)0.0000002 63. E- 7 65. 2 E 7 67. 1 E 1 69.
- 77.2,000,000,000
- 83.about or
0.276, lb 85. or 359, sec 87.$76.26 89.$40,000
- 83.about or
- 93.about $1,220,000,000,000 95.$3252
- 19 101. 64
Section 5.4 (pages 325–329)
1.4; 6 3. 9 5. 19 7. 0 9.1; 6 11.1; 1 13.2; ,
15.3; 1, 8, 5 17. 19. 21.It cannot be simplified.
- 29.already simplified; 4;
binomial 31. ; 4; trinomial 33. ; 4; monomial
35.7; 0; monomial 37. (a) (b) 0 39. (a) 14 (b)
- 29.already simplified; 4;
- (a) 36 (b) 43. 45.
- 57.Answers will vary. 59. 61.
- 8 t^2 + 8 t+ 13 85. (a) 23 y+ 5 t (b)25°,, 67°88° 87.- 7 x- 1
- 3 x^2 y- 15 xy- 3 xy^28 x^2 + 8 x+ 6 2 x^2 + 8 x
- 6 x^2 - 12 x+ 12 - 10 4 b- 5 c 6 x-xy- 7
- 11 y^4 + 8 y^2 +y a^4 - a^2 + 1 5 m^2 + 8 m- 10
5 m^2 - 14 m+ 6 4 x^3 + 2 x^2 + 5 x4 x^4 - 4 x^2 + 4 x 15 m^3 - 13 m^2 + 8 m+ 11(^76) x (^2) - 152 x+ 65 6 m (^3) +m (^2) + 4 m- 14 3 y (^3) - 11 y 2
- 12 5 x^2 - 2 x 5 m^2 + 3 m+ 2
- 3 - 19
11 m^4 - 7 m^3 - 3 m^2 x^4- 5 x^55 p^9 + 4 p^7 - 2 xy^2
2 m^5 - r^5- 19 - 1
2 x- 361.5* 1017 mi3.59* 102 ,3.305* 109 $2.81* 1010 2.76* 10 -^1 ,9.2* 10 -^36 * 109 1 * 10104.7 1.04* 108- 3 106 - 3,000,000 2 10 -^7
1.3* 10 -^55 * 1023 * 10 -^4 - 4 * 10 -2.4* 102 6.3* 10 -^2- 6 * 104 -
6 * 1011 1.5* 107- 0.004 -810,000
2.03* 10 -^3 - 1.3* 107 - 6 * 10 -^36.02* 1023 5.876* 109 8.235* 104 7 * 10 -^62.3* 10 -^48 * 101 4 * 10 -^35.6* 106+3.0 -1.0A-12 Answers to Selected Exercises
89.0, , , , 0x5 y–2 0
–42
y = x^2 – 4- 3 - 4 - 3 91.7, 1, , 1, 7
xy27y = 2x^2 – 1- 1 93.0, 3, 4, 3, 0
xy04–3–2 2y = –x^2 + 4http://www.ebook777.com
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