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Unit 7
Algebra I
COMPETENCY 1: Zero and Negative
Exponents
For questions 1-10, simplify each expression.
1. 4x0
2. -3x0
0
3. -2x
4. -5x0
0
5. 2x
6. -50
0
7. -4
8. -70
0
9. 6
10. 50
For questions 11-40, evaluate each expression.
11. 3-2
12. 2-3
13. 4-2
14. 5-3
15. 2-2
1
17.  
2
3
2
1
16.  
2
2
1
18.  
3
3
53. Given that a =
54. Given that a =
55. Given that a =
56. Given that a =
58. Given that a =
1
20.  
4
22. (-3)-3
24. (-4)-2
26. -2-2
28. -2-4
30. -5-3
59. Given that a =
60. Given that a =
 1
31.   
 2
2
 1
32.   
 3
2
 1
33.   
 4
3
 1
34.   
 3
3
 1
35.   
 2
3
1
36.   
2
2
1
37.   
3
2
1
38.   
4
3
1
39.   
3
3
1
40.   
2
3
For questions 41-50, simplify so that the
expression only contains positive exponents.
41. a-3 b4 c5
42. x-2 y3 x-4
43. r-3 s5 t--2
44. d-6 e-3 f5
1
45. h5 g6 k-3
46.
3 4 2
a b c
1
1
47.
48.
3 2 3
5  6 2
x y z
r s t
1
1
49.
50.
k 3 f 4 g 5
h 3 g  4 f 2
51. Given that a =
52. Given that a =
57. Given that a =
3
1
19.  
3
21. (-2)-2
23. (-2)-4
25. (-5)-3
27. -3-3
29. -4-2
J. Baker
1
, evaluate: a-1
2
1
, evaluate:
2
1
, evaluate:
2
1
, evaluate:
2
1
, evaluate:
2
1
, evaluate:
3
1
, evaluate:
2
1
, evaluate:
3
1
, evaluate:
3
1
, evaluate:
4
a-2
a3
a2
a1
a-3
a-5
a-2
a2
a-2
COMPETENCY 2: Multiplication Property of
Exponents
Simplify each expression.
61. (3xy2z)(2x3yz)
62. 5a2b)(2ab3c)
5 6
2
63. (x y )(3xyz )
64. 2r5s3t)(3rs4t)
3
2
5 3
65. (3v wy )(4vw y )
66. (-y3)(6x2y)
67. (-3a3b5)(2a2b4)
68. (2x3y4)(-y5)
69. (-6x3y7)(2xy2)
70. (-x2y3)(2x3y3)
-3 -4
-3 5
71. (3x y )(-2x y )
72. (-2x2y-5)(x-3y-4)
-2 3
-2
73. (7a b )(-4a b)
74. (-3a-5b)(8ab-4)
-3 -4
2
75. (5r s )(-2r s)
76. (7x-1y3)(-3x4y-5)
-5
-3 -3
77. (-xy z)(2x yz )
78. (-4a-3b-4)(2a-3b-4)
-3
5 -6
79. (-3s t)(7s t )
80. (-8r3st--3)(2s3t)
3 2
81. (3x )
82. (4x3y2)3
83. (5a3b4)2
84. (3rs3t)3
 x5y 

86. 
 2 


5 6 3
85. (2rs t )
 r 3s 5
87. 
 3





3
2
 g3h 2 

89. 
 4 


91. (2r3s4)-3
93. (4x3y2)-3
2 2 -3
95. (5r s )
 2
97.  2
 3x



3
2
 a2b 3
88. 
 2





3
 r 2s3t 

90. 
 2 


92. (3x3y4)-2
94. (2x2y5)-2
 1 
96. 

 2x 
3
2
 1
98. 
 4 xy 2





2
Unit 7
Algebra I
2
 1 
99.  3 
 3x 
101. (3a2b3)2(-ab2)103. (5x3y)-2(2xy3)
105. (5a-3b2)2(3a2b-3)-2
107. (xy)3(2x2y)-2
109. (2rs3t)2(3r5t)-2
3
 3 

100. 
 5x 2 y 2 


102. (2x2y-2)2(3x2y3)2
104. (2a-2b-3)2(3ab2)-3
106. (2x)-2(3x2y)2
108. (3a2b3)-2(a2b2)-3
110. (3x2y-2)-2(xy)3
COMPETENCY 3: Division Property of
Exponents
Simplify each expression.
111.
113.
115.
117.
119.
121.
123.
125.
a5b
112.
a2b 5
 12 x 5 y 2
 6x 2 y 3
x6y7
xy 6
 x 2 y 2z2
 45 cd
9x 9 y 4 z
3xy
116.
12 x 2 y
 2 xy
3
a 3 b 4
5 y 3
122.
 20 xy
a5b 6
2mn 2
124.
10m 2 n
5 x 3 y 3
30 xy
129.
20 x 3 y 4
24 xy
126.
128.
130.
x 3 y 5
132.
x5y6
3x 2 y 5
134.
6 x 5 y 3
12 xy
16 x 3 y  4
5 6
137.
54 r s t
120.
5r t
10rt
135.
2a 2 b 3
 9c 3 d 6
127.
133.
16 ab 4
2 4 10
2 3
131.
 3a 2
114.
118.
x 4 y 3z
 18a 3 b
8r s
t
3  4
 2rs t
136.
138.
 9s 3 t 4
 4 x 3 y 2
12 x 2 y 3
6d 2 e 2
139.
J. Baker
 x 6 y 7 z 6
x 1 yz 1
 ab 
141.  
 c 
2
143.  
d
9
3
m
145.  2 
n 
7
r 6 s 5 t 5
140.
r 3 s 4 t
 2x 5
142. 
 y





 5c 
144.  6 
d 
2
 3a 2 b 

146. 
 c3 


 3ab 2
149. 
 c2





 3x 2
151. 
 y





2
 2a 2
152. 
 b3





3
 4b 3
153. 
 c4





2
 5x 3
154. 
 y





2
2
 2x 5
148. 
 y4





 x3
150. 
 y4

3
3
 3 x 5 y 

156. 
 6 xy 4 


 xy 6 

157. 
 x 3 y 


3
 2a 2 b 3 

158. 
  4a 5 b 


2
 3x 3 y  6
160. 
 5 x 2 y 3





a 3 b 4
a 2 b
 5a 3 b 5
15a 5 b
 18 x 4 y 5
3x  3 y
3x
6
15 x
3
y z
7
y5




2
COMPETENCY 4: Scientific Notation
16 x 5 y 3




 2x 5 y 

155. 
 xy 2 


 5n 3 s 2
 12 x 10 y 6
2
5
40n 2 s 3
 24 d e
4
3
 b2c 

147. 
 d3 


 3a 2 b 3
159. 
 4b 5

4
3
3
2
For question 161-170, write the following numbers in
scientific notation.
161.
163.
165.
167.
169.
.0034
.002
.089
34.67
81,324,000
162.
164.
166.
168.
170.
.3897
.00347
2,181,000
78,000,000
246
For questions 171-180, write the following numbers in
standard notation:
171.
173.
175.
177.
179.
3.6 x 10-2
3.496 x 10-3
5 x 10-4
2.894 x 102
8.11 x 104
172.
174.
176.
178.
180.
2.87 x 10-5
4 x 10-7
3.67 x 101
2.3 x 105
3.467 x 105
Unit 7
Algebra I
For questions 181-210, calculate and write your
answer in scientific notation.
181.
183.
185.
187.
189.
4(2x105)
8(2.32x104)
5(3.51x107)
7(3.267x10-7)
4(6.759x10-1)
182.
184.
186.
188.
190.
2(3x10-2)
3(3.4x10-3)
8(6.3x10-2)
5(3.6x102)
2(8.113x104)
191.
8x10 5
2
192.
3.6 x10 3
3
193.
8.24 x10 5
2
194.
9.39 x10 3
3
195.
1.25 x10 5
25
196.
3.6 x10 4
18
197.
3.61x10 5
19
198.
1.8x10 4
6
199.
201.
203.
205.
2.52 x10 6
4
5 x10 6
2.5 x10 4
5.7 x10
200.
202.
3
1.9 x10  4
2.25 x10 10
1.5x10 15
207. (9x108)(2x103)
209. (7.5x10-1)(2x103)
204.
6.34 x10 2
2
9.6 x10 7
1.2 x10 3
7.2 x10 5
9 x10 8
206. (2x103)(4x105)
208. (8x105)(7x10-2)
210. (2x10-4)(5x102)
COMPETENCY 5: Distributed Practice
Write a statement using the word depends
to relate the following phrases.
1. cost of a pizza; amount of toppings
2. hours worked; amount paid
3. area of a square; length of a side
4. area of a circle; length of radius
5. type of tree; height of a tree
6. calories burned; type of exercise
7. Number of magazines sold; profit made
8. size of a garment; amount of material
used
9. temperature; geographic location
10. amount of oxygen; elevation
Find the range of each function given
that the domain = {-3, 0, 2}
11. f(x) = -2x - 2
12. f(x) = 3x2
13. f(x) = |x + 2|
14. f(x) = x - 3
15. f(x) = x2 - 2
16. f(x) = |-2x|
17. f(x) = 2x + 4
18. f(x) = 2x2 - 1
19. f(x) = |3 - x|
20. f(x) = -4x
J. Baker
21. Can the ordered pairs represent a function?
(-2, 1); (1, 0); (3, 2); (4, 1); (2, 0); (-1, 0)
22. Can the ordered pairs represent a function?
(-3, -4); (-2, -1); (2, 1); (3, 4); (-3, 5); (-4, -5)
23. Can the ordered pairs represent a function?
(-2, -1); (-1, 0); (4, 0); (3, -2); (5, -3); (-4, -5)
24. Can the ordered pairs represent a function?
(4, 1); (3, 1); (2, 1); (-1, 1); (5, 1); (-3, 1)
25. Can the ordered pairs represent a function?
(-4, -5); (-2, -1); (0, -2); (3, 4); (2, 5); (-3, -3)
26. Can the ordered pairs represent a function?
(1, 3); (1, 4); (1, 5); (1, -1); (1, -2); (1, 1)
27. Can the ordered pairs represent a function?
(2, 3); (-1, 5); (-1, 4); (2, 4); (3, 5); (3, -2)
28. Can the ordered pairs represent a function?
(4, 0); (3, -2); (2, -2); (4, -1); (3, 0); (-2, -1)
29. Can the ordered pairs represent a function?
(-1, -3); (-3, -4); (-2, 4); (3, -3); (4, 0); (0, 4)
30. Can the ordered pairs represent a function?
(0, 6); (-3, 0); (4, 5); (5, 0); (-3, 4); (2, -3)