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WorksheetsLaws of Exponents
Total questions: 66
Worksheet time: 3hrs 55mins
Name
Class
Date
1.
According to exponent rules, when we multiply the same base we _______ the exponents.
a)
Multiply
b)
Add
c)
Divide
d)
Subtract
2.
When dividing exponential expressions with the same base, what always happens to the exponents?
a)
they are added together
b)
they are subtracted
c)
they are divided
d)
they are multiplied
3.
When multiplying exponential expressions with the same base, what always happens to the exponents?
a)
they are added together
b)
they are subtracted
c)
they are divided
d)
they are multiplied
4.
Which is the expanded version of: 3x3y5x2
a)
3*x*x*x*y*y*y*y*y*x*x
b)
3*x*y*x
c)
3*3*3*x*x*x*y*y*y*y*y*x*x
5.
Complete the following statement to represent the quotient rule:
xa / xb = ?
xa / xb = ?
a)
xa + b
b)
xa x b
c)
xa - b
d)
abx
6.
According to exponent rules, when we raise the power to a power we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
7.
Simplify the expression.
(x5 )(x5)
(x5 )(x5)
a)
x10
b)
x25
c)
x16
d)
x8
8.
Simplify (c5)(c2)(c2)
a)
c20
b)
c9
c)
c11
d)
3c45
9.
Simplify the expression.
a)
214 z13
b)
22/z7
c)
214/ z7
d)
22 z7
10.
Simplify
a)
A
b)
B
c)
C
d)
D
11.
Simplify:
a)
A
b)
B
c)
C
d)
D
12.
2.) Simplify
(3x3y5)4
(3x3y5)4
a)
3x12y20
b)
81x12y20
c)
12x12y20
d)
81x7y9
13.
Simplify.
s-5 ⋅ s-2
s-5 ⋅ s-2
a)
s-3
b)
1/s7
c)
s-7
d)
1/s3
14.
Simplify (-9)0
a)
-9
b)
-1
c)
1
d)
9
15.
Simplify
(7x4)(9x3)
(7x4)(9x3)
a)
16x12
b)
79 x12
c)
63x7
d)
63x12
16.
Simplify
(2a2b4z)(6a3b2z5)
(2a2b4z)(6a3b2z5)
a)
8a5b6z6
b)
12a6b8z5
c)
12a5b6z6
d)
8a6b8z5
17.
Anything raised to a power of zero is always:
a)
0
b)
1
c)
itself
d)
negative
18.
(3x2y-5)(-6x4y3)
a)
-18x-2y-8
b)
-18x6/y2
c)
x6/18y2
19.
(34x5y6z-7)0
a)
34x5y6 / z7
b)
34x5y6 / x-7
c)
0
d)
1
20.
Write with positive exponents:
a)
a-2
b)
a2
c)
1/a1
21.
Change to radical form:
(2c)3/2
(2c)3/2
a)
√(2c)3
b)
∛(2c)2
c)
∛(2c)3
d)
√(2c)2
22.
Change to exponent form:
∛(p)5
∛(p)5
a)
p5/3
b)
p3/5
c)
p8
d)
p2
23.
Change to radical form:
√(4t)
√(4t)
a)
t4/2
b)
(4t)1
c)
t1/4
d)
(4t)1/2
24.
(y9)-2
a)
y18
b)
y11
c)
1/y18
d)
y9/2
25.
Simplify
(3x3y5)4
(3x3y5)4
a)
3x12y20
b)
81x12y20
c)
12x12y20
d)
81x7y9
26.
True or False: In the product of powers rule, you multiply the exponents when you have like bases.
a)
true
b)
false
27.
Write the exponent form of this expression: (x⋅x⋅x)⋅(x⋅x)
a)
3x⋅2x
b)
5x
c)
x5
28.
t63•t
a)
t64
b)
t63
29.
(2x2)2(3x3)3
a)
36x10
b)
36x13
c)
96x13
d)
96x10
30.
a)
49
b)
444
c)
421
d)
415
31.
a)
2a2b6
b)
1/2a2b6
c)
b6/2a2
d)
2b6/a2
32.
Which exponent rule is shown here?
w7⋅w9 = w7 + 9 = w16
w7⋅w9 = w7 + 9 = w16
a)
Product of Powers Rule
b)
Power to power Rule
c)
Quotient Rule
d)
Negative Exponent Rule
33.
Which exponent rule is shown here?
y-19 = 1/y19
y-19 = 1/y19
a)
Product of Powers Rule
b)
Power to power Rule
c)
Quotient Rule
d)
Negative Exponent Rule
34.
Which of the following equations is true?
a)
83 ⋅ 84 = 812
b)
150 = 0
c)
78/74 = 72
d)
5-2 = 1/25
35.
How do you solve:
2x56x4
a)
MULTIPLY coefficients
MULTIPLY exponents
b)
DIVIDE coefficients
SUBTRACT exponents
c)
Combine like terms
d)
MULTIPLY coefficients
ADD exponents
36.
Billy was asked to solve 35∙34. He got 920. What error did he make?
a)
When he multiplies exponents, he is supposed to add the base and the exponent
b)
When he multiplies exponents, he is supposed to multiply the base and keep the exponents
c)
When he multiplies exponents, he is supposed to keep the base and add the exponents if the base is the same
d)
None of the above
37.
Simplify:
a)
b)
c)
d)
38.
Simplify √75.
a)
5
b)
5√3
c)
3√5
d)
25√3
39.
Simplify:
a)
2√12
b)
4√12
c)
4√3
d)
16√3
40.
Simplify completely.
a)
5√6
b)
25√6
c)
√30
d)
15√10
41.
Simplify completely.
a)
4√8
b)
4√128
c)
32√2
d)
32√4
42.
Write as a radical expression
y²⁄ ³
y²⁄ ³
a)
2y³
b)
√y³
c)
∛y²
d)
3y²
43.
Simplify:
a)
2
b)
8
c)
16
d)
32
44.
Simplify the exponential expression:
a)
10x-2
b)
2x2
c)
2x12
d)
10x12
45.
Which is greater, 26540 or 50?
a)
26540
b)
50
c)
They are the same
d)
Zero is greater
46.
8 + 3(5 + 2) - 7 ∙ 2
a)
3
b)
15
c)
44
47.
27 ÷ 3 x 2 + 42
a)
34
b)
20.5
c)
26
48.
Find and explain the error.
5 - 3 + 2
5 - 5
0
5 - 3 + 2
5 - 5
0
a)
There is no error.
b)
Addition was done first and you should have subtracted first
c)
There is a subtraction error
49.
Simplify:
[25-(13+4)+4] ÷ 3
[25-(13+4)+4] ÷ 3
a)
6
b)
2
c)
3
d)
4
50.
Who's the Richest?
Four friends have all been saving money. Brad has more than Adam but not as much as George. Jenny has more than George. List in order of who has the least to the greatest.
Four friends have all been saving money. Brad has more than Adam but not as much as George. Jenny has more than George. List in order of who has the least to the greatest.
a)
Adam, Jenny, George, Brad
b)
Jenny, Adam, George, Brad
c)
Adam, Brad, George, Jenny
d)
Jenny, George, Brad, Adam
51.
(34x5y6z-7)0
a)
34x5y6 / z7
b)
34x5y6 / x-7
c)
0
d)
1
52.
8x2 + 9x - 10 + 2x2 + 4x + 15
a)
10X2 + 13x - 25
b)
10x2 + 13x + 25
c)
10x2 + 13x + 5
53.
CHALLENGE QUESTION!
Simplify the following expression:
(5x4 - 3x + 8x2) - (8x4 - 7x2)
Simplify the following expression:
(5x4 - 3x + 8x2) - (8x4 - 7x2)
a)
13x4 - 3x + 1x2
b)
-3x4 + 15x2 - 3x
c)
-3x4 - 1x2 + 3x
d)
13x4 + 15x2 - 3x
54.
0 - 16
a)
16
b)
0
c)
-16
d)
5
55.
(-7)(8)
a)
56
b)
-56
c)
1
d)
-1
56.
-10+4
a)
-14
b)
14
c)
-6
d)
6
57.
18 - (-4)
a)
-22
b)
4
c)
22
d)
-4
58.
8 - 12
a)
4
b)
-4
c)
-6
d)
-8
59.
-2 - (-8)
a)
6
b)
-6
c)
-10
d)
10
60.
-3(-4)
a)
-12
b)
7
c)
-7
d)
12
61.
-10(4)
a)
40
b)
-14
c)
-40
d)
14
62.
-27 / -27
a)
0
b)
-0
c)
1
d)
-1
63.
-4 - 1
a)
5
b)
-5
c)
3
d)
-3
64.
-12 - (-7) =
a)
-19
b)
5
c)
-5
d)
13
65.
1-2
a)
1
b)
-1
c)
3
d)
-3
66.
What is -29 - 11?
a)
40
b)
-12
c)
-18
d)
-40
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