Font size
S
M
L
XL
Worksheets2 Exponents Rat to Rad and Rad to Rat
Total questions: 150
Worksheet time: 9hrs 0mins
Name
Class
Date
1.
simplify 5x3 2x2
a)
10x5
b)
3x
c)
10x6
d)
7x5
2.
What is [ (12x3y5z7)/ (144x-4 y7z-3)]0
a)
12(x7z10)
b)
(x7z10)/12y2
c)
1
d)
(x7y-2z10)/12
3.
∛512 = ?
a)
≈177
b)
-8
c)
-8, 8
d)
8
4.
What is the cube root of -216?
a)
72
b)
-72
c)
-6
d)
6
5.
Solve -4x2 = -36
a)
+, - 9
b)
+, - 3
c)
9
d)
3
6.
evaluate ∛64
a)
-4
b)
4
c)
21.333
d)
-21.3333
7.
Simplify m12/ m3
a)
m12-3 = m9
b)
m12/3 = m4
c)
m-9
d)
-m9
8.
Simplify (7x4)(9x3)
a)
16x12
b)
79 x12
c)
63x4+3 = 63x7
d)
63x12 noooo oh nooooo
9.
simplify 7-2
a)
1/72 = 1/49
b)
-49
c)
-14
d)
1/14
10.
Simplify and leave in exponent form
82/85
82/85
a)
83
b)
82-5 = 8-3 = 1/83
c)
8-3
d)
87
11.
which is/are equivalent to 55 ?
54⋅50 54⋅51 54⋅52 56⋅5-1
54⋅50 54⋅51 54⋅52 56⋅5-1
a)
54⋅50 54⋅51
b)
54⋅51 54⋅52
c)
54⋅52 56⋅5-1
d)
54⋅51 56⋅5-1
12.
The amount of bacteria in an infection n hours after taking medication is (1/x3)n .
Write a simplified expression that represents the amount of bacteria in an infection 4 hours after taking medication.
Write a simplified expression that represents the amount of bacteria in an infection 4 hours after taking medication.
a)
(1/x3)4
b)
(1/x3)-4
c)
(1/x7)
d)
(1/x3)4 = (14) / (x3 times4) = 1/x12
13.
solve b2=56
a)
about -23
b)
about 23
c)
about 7.5 or -7.5
d)
about -7.5
14.
Write each expression in exponential form.
a)
A
b)
B
c)
C
d)
D
15.
Write each expression in exponential form.
a)
A
b)
B
c)
C
d)
D
16.
Write each expression in exponential form.
a)
A
b)
B
c)
C
d)
D
17.
Rewrite in Exponential Form.
a)
A
b)
B
c)
C
d)
D
18.
Rewrite in Exponential Form.
a)
A
b)
B
c)
C
d)
D
19.
Rewrite in radical form.
a)
A
b)
B
c)
C
d)
D
20.
Rewrite in Radical Form.
a)
A
b)
B
c)
C
d)
D
21.
Which is equivalent to √121p5r7s4?
a)
11prs √pr
b)
11p2.5r3.5s2 √pr
c)
11p2r3s2 √pr
d)
11p2r3s2
22.
Simplify:
a)
8x9
b)
8x3
c)
8x4√x
d)
8x3√x
23.
Write each expression in exponential form.
a)
A
b)
B
c)
C
d)
D
24.
Write each expression in exponential form.
a)
A
b)
B
c)
C
d)
D
25.
Write each expression in exponential form.
a)
A
b)
B
c)
C
d)
D
26.
Rewrite in radical form.
a)
A
b)
B
c)
C
d)
D
27.
Rewrite in Radical Form.
a)
A
b)
B
c)
C
d)
D
28.
Rewrite in Exponential Form.
a)
A
b)
B
c)
C
d)
D
29.
Rewrite in Exponential Form.
a)
A
b)
B
c)
C
d)
D
30.
Simplify the expression:
31/3 * 91/3
31/3 * 91/3
a)
3
b)
9
c)
1/3
d)
27
31.
Simplify the expression:
31/2 * 271/2
31/2 * 271/2
a)
9
b)
81
c)
3
d)
1/3
32.
Simplify the expression:
101/2 * 101/2
101/2 * 101/2
a)
10
b)
100
c)
10,000
d)
3.56
33.
Simplify the expression:
271/3
271/3
a)
3
b)
9
c)
27
d)
33
34.
Simplify the expression:
361/2
361/2
a)
6
b)
36
c)
-6
d)
1296
35.
Write the expression in radical form.
x7/2
x7/2
a)
√x7
b)
7√x2
c)
7x2
d)
∛x7
36.
Write the expression in radical form.
x1.5
x1.5
a)
√x3
b)
∛x2
c)
x3
d)
√x
37.
Write the expression in radical form.
y1/2
y1/2
a)
√y
b)
∛y
c)
√y2
d)
∛y2
38.
Write the expression in radical form.
x3/4
x3/4
a)
∜x3
b)
∛x4
c)
x.75
d)
√x2
39.
Write the expression in exponential form:
∛(2x)2
∛(2x)2
a)
(2x)2/3
b)
2x2/3
c)
2x3/2
d)
(2x)3/2
40.
Write the expression in exponential form:
∜x5
∜x5
a)
x4/5
b)
x5/4
c)
x5
d)
x1/4
41.
Write the expression in exponential form:
∛x2
∛x2
a)
x3/2
b)
x2/3
c)
x1/2
d)
x1/3
42.
Write the expression in exponential form:
√23
√23
a)
231/2
b)
23-1/2
c)
232
d)
23-2
43.
Re-write the expression in the most simplified exponential form.
(∜y)10
(∜y)10
a)
y10/4
b)
y2/5
c)
y14
d)
y5/2
44.
Simplify the expression completely and write in radical form if necessary.
(x2/3)6
(x2/3)6
a)
∛x2
b)
∛x20
c)
x4
d)
√x3
45.
Simplify the expression completely and write it in radical form if necessary.
x3/4⋅x1/2
x3/4⋅x1/2
a)
x
b)
∜x5
c)
√x
d)
∜x2
46.
Re-write the expression in radical form.
x2/3
x2/3
a)
∛x2
b)
√x3
c)
(1/x)
d)
∛x
47.
Write in exponential form
∛x⁷
∛x⁷
a)
x⁷/³
b)
x3⁄7
c)
3x⁷
d)
7x³
48.
What is 80 ?
a)
1
b)
8
c)
0
d)
Psh..... I don't know. I'm not a math teacher.
49.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
50.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
51.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
52.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
53.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
54.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
55.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
56.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
57.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
58.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
59.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
60.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
61.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
62.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
63.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
64.
Write each expression in radical form.
a)
A
b)
B
c)
C
d)
D
65.
Write each expression in radical form.
a)
A
b)
B
c)
C
d)
D
66.
Write each expression in radical form.
a)
A
b)
B
c)
C
d)
D
67.
Write each expression in radical form.
a)
A
b)
B
c)
C
d)
D
68.
Write each expression in exponential form.
a)
A
b)
B
c)
C
d)
D
69.
Write each expression in exponential form.
a)
A
b)
B
c)
C
d)
D
70.
Write each expression in exponential form.
a)
A
b)
B
c)
C
d)
D
71.
Write each expression in exponential form.
a)
A
b)
B
c)
C
d)
D
72.
Simplify
a)
A
b)
B
c)
C
d)
D
73.
Simplify
a)
A
b)
B
c)
C
d)
D
74.
Simplify
a)
A
b)
B
c)
C
d)
D
75.
Simplify
a)
A
b)
B
c)
C
d)
D
76.
Simplify
a)
A
b)
B
c)
C
d)
D
77.
Simplify
a)
A
b)
B
c)
C
d)
D
78.
Simplify
a)
A
b)
B
c)
C
d)
D
79.
Simplify. Your answer should only contain positive exponents.
a)
A
b)
B
c)
C
d)
D
80.
Write in exponential form
√x⁵
√x⁵
a)
X¹∕ ⁵
b)
X ²⁄⁵
c)
X⁵⁄ ²
d)
X⁵
81.
Write in exponential form
∜(3x)³
∜(3x)³
a)
3x³⁄ ⁴
b)
(3x)³∕ ⁴
c)
(3x)⁴⁄ ³
d)
3x⁴⁄ ³
82.
Write as a radical expression
y²⁄ ³
y²⁄ ³
a)
2y³
b)
√y³
c)
∛y²
d)
3y²
83.
Write as a radical expression
y¹⁄ ³
y¹⁄ ³
a)
∛y
b)
y³
c)
√y
d)
1∕ 3y
84.
Simplify
x²⁄ ³⋅x¹⁄ ³
x²⁄ ³⋅x¹⁄ ³
a)
2x
b)
x²⁄₉
c)
x
d)
x²
85.
Simplify:
x⁻ ¹⁄ ² ⋅ x⁻¹⁄ ⁴
x⁻ ¹⁄ ² ⋅ x⁻¹⁄ ⁴
a)
-x¹∕ ⁶
b)
x ³∕ ⁴
c)
1∕ x³⁄⁴
d)
x¹∕ ⁸
86.
Simplify
(x²⁄ ³)²⁄ ⁵
(x²⁄ ³)²⁄ ⁵
a)
x⁴∕ ¹⁵
b)
x¹⁶∕ ¹⁵
c)
x⁶
d)
6x
87.
Simplify
(x⁻²)⁻¹∕²
(x⁻²)⁻¹∕²
a)
1∕ x³∕²
b)
1∕ x²
c)
1∕ x
d)
x
88.
Simplify
x⅞ ⁄ x
x⅞ ⁄ x
a)
x
b)
1∕ x¹∕ ⁸
c)
1∕8x
d)
x⁴
89.
Write in exponential form
∛x⁷
∛x⁷
a)
x⁷∕ ³
b)
x3⁄7
c)
3x⁷
d)
7x³
90.
Write the expression in exponential form:
√23
√23
a)
231/2
b)
23-1/2
c)
232
d)
23-2
91.
Write the expression in exponential form:
∜x5
∜x5
a)
x4/5
b)
x5/4
c)
x5
d)
x1/4
92.
Write the expression in exponential form:
∛x2
∛x2
a)
x3/2
b)
x2/3
c)
x1/2
d)
x1/3
93.
Write the expression in radical form.
x3/4
x3/4
a)
∜x3
b)
∛x4
c)
x.75
d)
√x2
94.
Write the expression in radical form.
x1.5
x1.5
a)
√x3
b)
∛x2
c)
x3
d)
√x
95.
Simplify the expression:
31/3 * 91/3
31/3 * 91/3
a)
3
b)
9
c)
1/3
d)
27
96.
Simplify the expression:
31/2 * 271/2
31/2 * 271/2
a)
9
b)
81
c)
3
d)
1/3
97.
Simplify the expression:
101/2 * 101/2
101/2 * 101/2
a)
10
b)
100
c)
10,000
d)
3.56
98.
Simplify the expression:
271/3
271/3
a)
3
b)
9
c)
27
d)
33
99.
Which is NOT the same as p2/3?
a)
(p1/3)2
b)
∛p2
c)
(p2)1/3
d)
√p3
100.
Evaluate 9-3/2
a)
1/27
b)
-27
c)
1/3
d)
-3
101.
Simplify.
a)
5x2
b)
5x1/2
c)
25x2
d)
5x12
102.
Simplify.
a)
5x6
b)
5x2
c)
5x3
d)
25x2
103.
Rewrite in radical form.
a)
A
b)
B
c)
C
d)
D
104.
Rewrite in Radical Form.
a)
A
b)
B
c)
C
d)
D
105.
8
a)
W
b)
O
c)
R
d)
K
106.
14
a)
a
b)
b
c)
c
d)
d
107.
14
a)
a
b)
b
c)
c
d)
d
108.
Rewrite the following as a radical. Simplify if possible.
a)
A
b)
B
c)
C
d)
D
109.
Simplify:
a)
2
b)
4
c)
16
d)
64
110.
Simplify the following expression:
a)
5
b)
25
c)
125
d)
625
111.
Simplify:
a)
2
b)
8
c)
16
d)
32
112.
Simplify:
a)
2
b)
4
c)
8
d)
16
113.
a)
44/3
b)
43/4
c)
24/3
d)
23/4
114.
a)
23/5
b)
-23/5
c)
25/3
d)
85
115.
Write in exponential form
√x⁵
√x⁵
a)
X¹∕ ⁵
b)
X ²⁄⁵
c)
X⁵⁄ ²
d)
X⁵
116.
Write in exponential form
∜(3x)³
∜(3x)³
a)
3x³⁄ ⁴
b)
(3x)³∕ ⁴
c)
(3x)⁴⁄ ³
d)
3x⁴⁄ ³
117.
Simplify
x²⁄ ³⋅x¹⁄ ³
x²⁄ ³⋅x¹⁄ ³
a)
2x
b)
x²⁄₉
c)
x
d)
x²
118.
a)
C
b)
A
c)
V
d)
E
119.
a)
A
b)
B
c)
C
d)
D
120.
a)
A
b)
B
c)
C
d)
D
121.
Simplify:
a)
2
b)
8
c)
16
d)
32
122.
Simplify the following expression:
a)
16
b)
32
c)
40
d)
64
123.
Simplify the following expression:
a)
2
b)
4
c)
16
d)
64
124.
Simplify the following expression:
a)
2
b)
4
c)
16
d)
64
125.
Simplify
(x²/³)²/⁵
(x²/³)²/⁵
a)
x⁴/¹⁵
b)
x¹⁶/¹⁵
c)
x⁶
d)
6x
126.
Write as a radical.
a)
a
b)
b
c)
c
d)
d
127.
Write as a radical.
a)
a
b)
b
c)
c
d)
d
128.
Write as a rational exponent.
a)
a
b)
b
c)
c
d)
d
129.
a)
A
b)
B
c)
C
d)
D
130.
a)
A
b)
B
c)
C
d)
D
131.
a)
A
b)
B
c)
C
d)
D
132.
a)
A
b)
B
c)
C
d)
D
133.
a)
A
b)
B
c)
C
d)
D
134.
a)
1/8
b)
-8
c)
4
d)
1/4
135.
Simplify the expression completely and write in radical form if necessary.
(x2/3)6
(x2/3)6
a)
∛x2
b)
∛x20
c)
x4
d)
√x3
136.
Simplify x2y-5
a)
x2/y5
b)
1/x2y5
c)
y5/x2
d)
x2/y-5
137.
Rewrite using a positive exponent.
w-13
w-13
a)
-w13
b)
1/w13
c)
1/w-13
d)
w13
138.
Write with positive exponents:
a)
a-2
b)
a2
c)
1/a1
139.
Simplify the exponential expression:
a)
10x-2
b)
2x2
c)
2x12
d)
10x12
140.
Write the expression in exponential form
a)
53/5
b)
35/3
c)
33/5
d)
55/3
410/3
410/3
141.
Write the expression in exponential form
a)
31/3
b)
33/1
c)
33/2
d)
32/3
142.
Write the expression in exponential form
a)
65/3
b)
36/5
c)
53/6
d)
35/6
143.
Write the expression in exponential form
a)
73/4
b)
43/7
c)
37/4
d)
74/3
144.
Write the expression in exponential form
a)
53/5
b)
33/5
c)
55/3
d)
5
145.
Simplify the expression completely
71/3 ⋅ 211/3
71/3 ⋅ 211/3
a)
21
b)
∛147
c)
7
d)
∛7
146.
Simplify the expression completely
491/2
491/2
a)
√49
b)
49²
c)
7
d)
√7
147.
Simplify the expression completely
21/2 ⋅ 321/2
21/2 ⋅ 321/2
a)
8
b)
√64
c)
√32
d)
64
148.
Simplify the expression completely
21/2 ⋅ 321/2
21/2 ⋅ 321/2
a)
8
b)
√64
c)
√32
d)
64
149.
Write the expression in exponential form
a)
53/5
b)
35/3
c)
33/5
d)
55/3
410/3
410/3
150.
Write the expression in exponential form
a)
31/3
b)
33/1
c)
33/2
d)
32/3
Reset
