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Law of exponents

Total questions: 93

Worksheet time: 2hrs 35mins

Name
Class
Date
1.
What's the base?
y5
a)
5
b)
y
2.
Which is the expanded form of 
53
a)
3 x 3 x 3
b)
5 x 5
c)
5 x 5 x 5
d)
5 x 3
3.
What is the exponential form of 
4 x 4 x 4 x 4 x 4 x 4
a)
64
b)
42
c)
46
d)
4 x 6
4.

Rewrite the following expression in exponential form:

2*2*2*5*5*5*5

a)

3*2*4*5

b)

8*625

c)

23*54

d)

32*45

5.

m*m*m*m*p*p*p*q*q*q*q*q

a)

4m*3p*5q

b)

m4p3q5

c)

4m3p5q

d)

12mpq

6.

According to exponent rules, when we multiply terms with the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

7.
Power to a Power Law states: keep the base the same and do this to the exponents.
a)
multiply
b)
add
c)
subtract
d)
divide
8.

According to exponent rules, when we divide the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

9.
Anything raised to a power of zero is always: 
a)
0
b)
1
c)
itself
d)
negative
10.

Simplify the following expression:

75 * 72 =

a)

77

b)

75

c)

499

11.
Simplify the expression:
(a5)(a4)
a)
a20
b)
a9
c)
a1
12.
Simplify the expression in exponential form:
(54)3
Hint: Expand it out
a)
51
b)
57
c)
512
13.
(y9)-2
a)
y18
b)
y11
c)
1/y18
d)
y9/2
14.
Simplify the expression:
(58) ÷ (52)
a)
56
b)
510
c)
54
d)
516
15.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
16.
Evaluate the expression using the quotient rule.
a)
x13
b)
x5
c)
x36
d)
x-5
17.

Which expression is NOT equivalent to  383^8 ?

a)

(36)(32)\left(3^6\right)\left(3^2\right)  

b)

(34)2\left(3^4\right)^2  

c)

(34)(34)\left(3^4\right)\left(3^4\right)  

d)

(34)4\left(3^4\right)^4  

18.

4554

a)

209

b)

Can't simplify

c)

201

19.
Simplify the expression in exponential form:
1340
a)
0
b)
134
c)
1
20.

z0

a)

z

b)

0

c)

1

21.

How do you feel rewriting expressions using the laws of exponents to generate equivalent expressions.

a)

Rules of exponents are easy.

b)

With a little of more practice I can master it.

c)

Need lots of practice. They are not that easy .

d)

I still don't get it. Those rules are really confusing.

22.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
23.
Simplify:
x5 ÷ x2
a)
x7
b)
x3
c)
x10
d)
x2.5
24.
Simplify:
(x3)(x2)
a)
x5
b)
x6
c)
x
d)
x1.5
25.
Simplify (-5.7)0
a)
1
b)
0
c)
-1
d)
-5.7
26.
a)
x12
b)
x-12
c)
x2
d)
x-2
27.
a)
w
b)
w-1= 1/w
c)
-w
d)
w17
28.
a)
a7
b)
a10
c)
a3
d)
a-3
29.
a)
3
b)
0
c)
1
d)
1/3
30.
a)
8
b)
1/8
c)
87
d)
all of the above
31.
According to exponent rules, when we multiply the same base we _______ the exponents.
a)
Multiply
b)
Add
c)
Divide
d)
Subtract
32.
According to exponent rules, when we divide the same base we _______ the exponents.
a)
Multiply
b)
Add
c)
Divide
d)
Subtract
33.
How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?
a)
57
b)
56
c)
75
d)
5
34.
Simplify:
b2 ⋅ b4
a)
b8
b)
b6
c)
b2
d)
2b6
35.
Simplify:
(x5)4
a)
x9
b)
x20
c)
x
d)
x54
36.
According to exponent rules, when we raise the power to a power we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
37.
n²⋅n⁴⋅n⁵
a)
n¹¹
b)
n⁴⁰
c)
n¹³
d)
n²²
38.
Multiply
a)
100
b)
101
c)
10-2
d)
1/100
39.
Anything raised to a power of zero is always: 
a)
0
b)
1
c)
itself
d)
negative
40.
Make this negative exponent positive.
9-3
a)
93
b)
1/9-3
c)
1/93
d)
729
41.
x-3
a)
1/x3
b)
1/x-3
c)
3x
d)
1/3x
42.

34 x 37

a)

928

b)

328

c)

311

d)

911

43.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
44.
(2ab)3
a)
23a3b3
b)
2ab3
c)
6a3b3
d)
6ab
45.
Simplify:
x5 ÷ x2
a)
x7
b)
x3
c)
x10
d)
x2.5
46.
Simplify:
(x3)(x2)
a)
x5
b)
x6
c)
x
d)
x1.5
47.
According to exponent rules, when we multiply the same base we _______ the exponents.
a)
Multiply
b)
Add
c)
Divide
d)
Subtract
48.
Make this negative exponent positive.
9-3
a)
93
b)
1/9-3
c)
1/93
d)
729
49.
According to exponent rules, when we divide the same base we _______ the exponents.
a)
Multiply
b)
Add
c)
Divide
d)
Subtract
50.
How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?
a)
57
b)
56
c)
75
d)
5
51.
Simplify (-1/2)0
a)
1
b)
0
c)
-1
d)
-2
52.
n²⋅n⁴⋅n⁵
a)
n¹¹
b)
n⁴⁰
c)
n¹³
d)
n²²
53.
a)
49
b)
444
c)
421
d)
415
54.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
55.
Make this negative exponent positive.
9-3
a)
93
b)
1/9-3
c)
1/93
d)
729
56.
According to exponent rules, when we multiply the same base we _______ the exponents.
a)
Multiply
b)
Add
c)
Divide
d)
Subtract
57.
According to exponent rules, when we divide the same base we _______ the exponents.
a)
Multiply
b)
Add
c)
Divide
d)
Subtract
58.
How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?
a)
57
b)
56
c)
75
d)
5
59.
Simplify:
b2 ⋅ b4
a)
b8
b)
b6
c)
b2
d)
2b6
60.
Simplify:
(x5)4
a)
x9
b)
x20
c)
x
d)
x54
61.
(x3y)6
a)
2x18y6
b)
x18y6
c)
x3y6
d)
x3y6
62.
Simplify (-1/2)0
a)
1
b)
0
c)
-1
d)
-2
63.
Simplify the following expression: 
xy-7
a)
xy7
b)
x/y7
c)
x7/y
d)
x7y
64.
According to exponent rules, when we raise the power to a power we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
65.
n²⋅n⁴⋅n⁵
a)
n¹¹
b)
n⁴⁰
c)
n¹³
d)
n²²
66.
Multiply
a)
100
b)
101
c)
10-2
d)
1/100
67.
a)
6-2
b)
1/62
c)
1/36
d)
All of the above
68.
a)
49
b)
444
c)
421
d)
415
69.
a)
0
b)
3
c)
1
d)
-1
70.
a)
w
b)
w-1= 1/w
c)
-w
d)
w17
71.
a)
a7
b)
a10
c)
a3
d)
a-3
72.
a)
2560
b)
2517
c)
560
d)
517
73.
a)
1
b)
60
c)
36/36
d)
all of the above
74.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
75.
(2ab)3
a)
23a3b3
b)
2ab3
c)
6a3b3
d)
6ab
76.

Evaluate the expression using the quotient rule.

a)

34

b)

134\frac{1}{3^4}

c)

3-12

d)

332

77.
Simplify:
(x3)(x2)
a)
x5
b)
x6
c)
x
d)
x1.5
78.
Simplify:
(3t2)3
a)
9t6
b)
9t5
c)
27t6
d)
27t5
79.
a)
-6c5
b)
-6c
c)
6c
d)
-6c6
80.
(6x2)(-3x5)
a)
18x7
b)
-18x7
c)
18x10
d)
3x7
81.

Make this negative exponent positive.

9-3

a)

93

b)

19−3\frac{1}{9^{-3}}

c)

193\frac{1}{9^3}

d)

729

82.
How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?
a)
57
b)
56
c)
75
d)
5
83.
a)

6-2

b)

162\frac{1}{6^2}

c)

136\frac{1}{36}

d)

All of the above

84.
a)
49
b)
444
c)
421
d)
415
85.
a)
a7
b)
a10
c)
a3
d)
a-3
86.
a)
5-8
b)
52
c)
25-8
d)
252
87.

Simplify the following expression:

x18y15x6y3\frac{x^{18}y^{15}}{x^6y^3}  

a)

x3y5

b)

x12y12

c)

x24y18

d)

x108y45

88.

Simplify the following expression:
30y1215y2\frac{30y^{12}}{15y^2}  

a)

2y24

b)

210

c)

2y10

d)

2y14

89.

Which expression is equivalent to the given?

a)
b)
c)
d)
90.
a)

a-3

b)

a3

c)

3a

d)


1a−3\frac{1}{a^{-3}}

91.
a)
b)
c)
d)
92.
a)
b)
c)
d)
93.
a)
b)
c)
d)

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