Page 1
1.
Simplify the expression. Express your answer using only positive exponents.
88
64
ab
ab
2.
Simplify the expression. Express your answer using only positive exponents.
9 –1
34
ab
ab
3.
Simplify the expression. Express your answer using only positive exponents.
–7 –4
–3 –6
ab
ab
4.
Simplify the expression. Express your answer using only positive exponents.
–7
–1 2
ab
ab
5.
Simplify the expression. Express your answer using only positive exponents.
( )( )
4 –4 –1 9
x y x y
6.
Simplify the expression. Express your answer using only positive exponents.
( )( )
6 7 –12
x y x y
7.
Simplify the expression. Express your answer using only positive exponents.
8.
Simplify the expression. Express your answer using only positive exponents.
( )( )
2 3 –9 –13
x y x y
9.
Simplify the expression. Express your answer using only positive exponents.
( )( )
4 7 3 –7
x y x y
Page 2
10.
Simplify the expression. Express your answer using only positive exponents.
( )( )
–5 –1 5 8
x y x y
11.
Simplify the expression. Express your answer using only positive exponents.
( )( )
2 –4 –2 –1
x y x y
12.
Simplify the expression. Express your answer using only positive exponents.
( )( )
–4 –1 2
x y x y
13.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
4
–2
2xy
14.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
5
2 –7
2xy
15.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
3
–5 –7
2xy
16.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
4
–3
3xy−
17.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
2
2 –7
3xy −
Page 3
18.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
5
63
2xy −
19.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
3
–6 –1
2xy −
20.
Simplify the expression. Express your answer using only positive exponents.
( )
–5
–4 –2
2
pp
p
21.
Simplify the expression. Express your answer using only positive exponents.
( )
5
5 –5
5
pp
p
22.
Simplify the expression. Express your answer using only positive exponents.
( )
0
23
2
pp
p
23.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
3
–4 6
–xy
24.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
4
–4
–xy
25.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
3
–2 –3
–xy
Page 4
26.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
5
–6
–2xy−
27.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
4
3 –1
–3xy −
28.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
3
57
–xy −
29.
Simplify the expression. Express your answer using only positive exponents and
evaluate whenever possible.
( )
5
–1 –2
–2xy −
30.
Simplify the expression. Express your answer using only positive exponents.
3
10 5
4 –1
ab
ab



31.
Simplify the expression. Express your answer using only positive exponents.
2
35
–1 –1
ab
ab
−



32.
Simplify the expression. Express your answer using only positive exponents.
4
5 –13
3 –7
ab
ab



33.
Simplify the expression. Express your answer using only positive exponents.
4
4 –1
–1
ab
ab
−



Page 5
34.
Simplify the expression. Express your answer using only positive exponents.
4
–7 2
–4 –4
ab
ab



35.
Simplify the expression. Express your answer using only positive exponents.
2
–8 4
–3 –2
ab
ab
−



36.
Simplify the expression. Express your answer using only positive exponents.
3
6 –11
7 –5
ab
ab



37.
Simplify the expression. Express your answer using only positive exponents.
2
–4 –3
22
ab
ab
−



38.
Simplify the expression. Express your answer using only positive exponents.
3
–1 9
–1 5
ab
ab



39.
Simplify the expression. Express your answer using only positive exponents.
2
5
5 –5
ab
ab
−



40.
Simplify the expression. Express your answer using only positive exponents.
5
4
ab
ab



41.
Simplify the expression. Express your answer using only positive exponents.
4
6 –7
6 –4
ab
ab
−



Page 6
42.
Simplify the expression. Express your answer using only positive exponents.
4
–3 4
–1 4
ab
ab



43.
Simplify the expression. Express your answer using only positive exponents.
4
–1 –2
2 –2
ab
ab
−



44.
Simplify the expression. Express your answer using only positive exponents.
2
–3
2 –3
ab
ab



45.
Simplify the expression. Express your answer using only positive exponents.
5
2 –2
3 –2
ab
ab
−



46.
Simplify the expression. Express your answer using only positive exponents.
( )
( )
–1
–4 –2
–1
4
ab
ab
47.
Simplify the expression. Express your answer using only positive exponents.
( )
( )
–2
–1 –3
3
2 –3
ab
ab
48.
Simplify the expression. Express your answer using only positive exponents.
( )
( )
–2
–5 –1
4
–5 2
ab
ab
Page 7
49.
Simplify the expression. Express your answer using only positive exponents.
( )
( )
2
–4
2
–2 2
ab
ab
50.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
(0.0032) (0.0059)
51.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
(0.0067) (0.0016)
52.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
( )( )
–4 –3
3.8 10 9.9 10••
53.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
( )( )
54
8.2 10 9.1 10••
54.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
–1
–5
1.265 10
5.5 10
55.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
–8
–3
7.968 10
8.3 10
56.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
240
0.0005
Page 8
57.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
19,800
0.00003
58.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
( )( )
( )
9 –12
–10
3 10 8 10
6 10

59.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
( )
5
6
3.7 10•
60.
Use scientific notation to perform each computation. Write your answers in scientific
notation.
( )
3
–3
3.3 10•
61.
Simplify and express the answer as a power of 10 with a positive exponent.
–6 –2
10 10•
62.
Simplify and express the answer as a power of 10 with a positive exponent.
–4
6
10
10
63.
Simplify and express the answer as a power of 10 with a positive exponent.
( )
5
–6
10
64.
Simplify the expression. Express your answer using only positive exponents.
( ) ( )
–6 7 –3 –5 –4 6
3 12 12 3x x x x x x− + −
Page 9
65.
Simplify the expression. Express your answer using only positive exponents.
( )
( )
5
–3
4+
4+
xy
xy
66.
Simplify the expression. Express your answer using only positive exponents.
( )
( )
–3
4
6+
6+
xy
xy
67.
Simplify the expression. Express your answer using only positive exponents.
–7 –2 –10
n n n••
68.
Simplify the expression. Express your answer using only positive exponents.
( )
( )
d
bc
j
gh
a
f
xy
xy
69.
Simplify the expression. Express your answer using only positive exponents.
0
77
6 –4
7
7
xy
xy



70.
Rewrite the expression using fractional exponents. Do not simplify.
( )
2
46y
71.
Evaluate the expression.
52
4
72.
Simplify the expression.
68
25xy
73.
Simplify the expression. Express the answer in radical form if necessary.
79
54xy
Page 10
74.
Simplify the expression.
38
12xy
75.
Simplify the expression.
47
75xy
76.
Simplify the expression.
10 6
18xy
77.
Simplify the expression.
16 13
3–xy
78.
Simplify the expression.
13 9
3192xy
79.
Simplify the expression.
12 11
3xy
80.
Simplify the expression.
15 9
316xy
81.
Simplify the expression. Express your answer using only positive exponents.
5 7 3
1 2 –1
ab
ab
82.
Simplify the expression. Express your answer using only positive exponents.
1 2 2
–1 –3 2
ab
ab
Page 11
83.
Simplify the expression. Express your answer using only positive exponents.
4 1 2
5 3 4
ab
ab
84.
Simplify the expression. Express your answer using only positive exponents.
–3 2 4
3 2 3
ab
ab
85.
Simplify the expression. Express your answer using only positive exponents.
( )( )
2 7 2 –5 3 –1
a b a b
86.
Simplify the expression. Express your answer using only positive exponents.
( )( )
3 2 3 1 3 –3
a b a b
87.
Simplify the expression. Express your answer using only positive exponents.
( )( )
–2 4 3 –5 2 3
a b a b
88.
Simplify the expression. Express your answer using only positive exponents.
( )( )
–3 4 3 4 5 –3
a b a b
89.
Simplify the expression. Express your answer using only positive exponents.
2
2 –14 5
3 4 –3
ab
ab



90.
Simplify the expression. Express your answer using only positive exponents.
2
5 3 5
–2 2 3
ab
ab



91.
Simplify the expression. Express your answer using only positive exponents.
2
4 –3 4
–5 4 3
ab
ab



Page 12
92.
Simplify the expression. Express your answer using only positive exponents.
3
25
2 –1 4
ab
ab



93.
Simplify the expression. Express your answer using only positive exponents.
2
3 7 4
5 3 –3
ab
ab
−



94.
Simplify the expression. Express your answer using only positive exponents.
2
–4 3 2
–2 –1 3
ab
ab
−



95.
Simplify the expression. Express your answer using only positive exponents.
3
3 5 4
3 5 3
ab
ab
−



96.
Simplify the expression. Express your answer using only positive exponents.
3
1 2 5
5 –2 5
ab
ab
−



97.
A period is the time it takes for one complete swing of a pendulum. The period T (in
seconds) of a swinging pendulum is found using the formula
232
L
T
=
where L is
the length of the pendulum in feet.
A) Find the period (in seconds) of a pendulum whose length is 2 feet 1 inches.
B) How long (in inches) would a pendulum have to be to have a period of 6 seconds?
Round answers to 2 decimal places.
98.
Evaluate:
12
100
99.
Evaluate:
12
a
Page 13
100.
Evaluate:
400
101.
Evaluate:
3–1,000
102.
Assume all variables represent positive quantities and simplify.
14 6
8
ab
c
103.
Assume all variables represent positive quantities and simplify.
24 12
312
ab
c
104.
Simplify by removing all possible factors from the radical, then combine any like terms.
6 78,125 – 4 3,125
105.
Simplify by removing all possible factors from the radical, then combine any like terms.
33
5 16 +3 128
106.
Simplify by removing all possible factors from the radical.
74
11
9
ab
c
107.
Simplify by removing all possible factors from the radical.
10 3
322
1331
ab
c
108.
Evaluate the expression.
10
9 10•
109.
Evaluate the expression.
8
2.89 10•
Page 14
110.
Evaluate the expression.
5
3.249 10•
111.
Calculate:
54
81
112.
Calculate:
13
125
8



113.
Find the length of a side, s, of a cube with volume, V, of 343 in3. (Where V = s3.)
114.
The time it takes for one complete swing of a pendulum is called the period of its
motion. The period T (in seconds) of a swinging pendulum is found using the formula
232
L
T
=
m where L is the length of the pendulum in feet and 32 is the acceleration of
gravity in feet per second.
Find the period of a pendulum whose length is 1 ft 4 in. (Round the answer to 3
decimal places.)
115.
The time it takes for one complete swing of a pendulum is called the period of its
motion. The period T (in seconds) of a swinging pendulum is found using the formula
232
L
T
=
seconds where L is the length of the pendulum in feet and 32 is the
acceleration of gravity in feet per second.
Find the length of a pendulum whose period is 2.421 seconds. (Express the answer in
feet and inches to the nearest inch.)
116.
Find the height of an equilateral triangle with side 2 cm. (Use the Pythagorean
theorem. Round the answer to 3 decimal places.)
Page 15
Answer Key
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