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Worksheets

Exponents Review

Total questions: 184

Worksheet time: 8hrs 2mins

Name
Class
Date
1.
Anything raised to a power of zero is always: 
a)
0
b)
1
c)
itself
d)
negative
2.
According to exponent rules, when we raise the power to a power we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
3.

According to exponent rules, when we multiply expressions with same bases we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

4.
According to exponent rules, when we divide powers we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
5.

Simplify the following expression:


-90

a)

-9

b)

0

c)

-1

d)

1

6.
x⁻⁶
a)
1 ⁄ x⁶
b)
x⁶
c)
-x⁶
d)
-1 ⁄ x⁶
7.

Simplify.

(2n4 )( 5n4)

a)

7n4

b)

10n16

c)

10n8

d)

none of the above

8.

Simplify.

a)

a8b13

b)

a2b7

c)

a15b30

d)

none of the above

9.
Simplify (-1/2)0
a)
1
b)
0
c)
-1
d)
-2
10.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
11.
Evaluate the expression using the quotient rule.
a)
1
b)
g10
c)
g25
d)
g
12.
(2x3y)6
a)
2x18y6
b)
64x18y6
c)
64x3y6
d)
2x3y6
13.

Simplify.

(52)3

a)

56

b)

55

c)

57

d)

58

14.

Simplify:

(6k2)(k)

a)

7k3

b)

7k2

c)

6k2

d)

6k3

15.

Simplify:

(2ab)3

a)

8a3b3

b)

2ab3

c)

6a3b3

d)

8ab

16.
Simplify the expression.
a)
9x3
b)
2x3
c)
2x4
d)
9x4
17.

Simplify: 8x2 + 3x2

a)

11x4

b)

24x4

c)

11x2

d)

24x4

18.

Simplify: 4y3 - 2y + y3

a)

3y

b)

3y3

c)

5y3-2y

d)

5

19.

Simply the following monomials. Express the final answer using positive exponents only!

292132^9\cdot2^{13}

20.

Simply the following monomials. Express the final answer using positive exponents only!

8858\cdot8^{-5}

21.

Simply the following monomials. Express the final answer using positive exponents only!

(10)6(10)6\left(-10\right)^6\cdot\left(-10\right)^{-6}

22.

Simply the following monomials. Express the final answer using positive exponents only!

x4x2x^4\cdot x^2

23.

Simply the following monomials. Express the final answer using positive exponents only!

x3x8x^3\cdot x^8

24.

Simply the following monomials. Express the final answer using positive exponents only!

x8x1x^8\cdot x^{-1}

25.

Simply the following monomials. Express the final answer using positive exponents only!

x5x7xx^5\cdot x^{-7}\cdot x

26.

Simply the following monomials. Express the final answer using positive exponents only!

x5y1x4x^{-5}\cdot y^{-1}\cdot x^4

27.

Simply the following monomials. Express the final answer using positive exponents only!

x2y1x11y6x^{-2}\cdot y^{-1}\cdot x^{11}\cdot y^{-6}

28.

Simply the following monomials. Express the final answer using positive exponents only!

5x47x35x^4\cdot7x^3

29.

Simply the following monomials. Express the final answer using positive exponents only!

(9x5)(2x2)\left(9x^5\right)\cdot\left(-2x^{-2}\right)

30.

Simply the following monomials. Express the final answer using positive exponents only!

4x33x10-4x^3\cdot-3x^{-10}

31.

Simply the following monomials. Express the final answer using positive exponents only!

(2xy)(5x8y3)\left(2xy\right)\cdot\left(5x^8y^3\right)

32.

Simply the following monomials. Express the final answer using positive exponents only!

23x2y1 18x3y\frac{2}{3}x^{-2}y^{-1}\cdot\ 18x^{-3}y

33.

Simply the following monomials. Express the final answer using positive exponents only!

23x2y1 18x3y\frac{2}{3}x^{-2}y^{-1}\cdot\ 18x^{-3}y

34.

Simplify using the Laws of Exponents

4842\frac{4^8}{4^2}  

a)

  464^6  

b)

4,000

c)

4104^{10}  

d)

24

35.

57 54\frac{5^7\ }{5^4}  

a)

535^3  

b)

100

c)

5115^{11}  

d)

535^{-3}  

36.

16t48t\frac{16t^4}{8t}  

a)

2t32t^3  

b)

8t58t^5  

c)

2t52t^5  

d)

245=402\cdot4\cdot5=40  

37.

4a5 (6a5)=-4a^{5\ }\left(6a^5\right)=  

a)

24a10-24a^{10}  

b)

10a0-10a^0  

c)

24a1024a^{10}  

d)

2a102a^{10}  

38.

Find the missing exponent (y)

3xy  4x3  = 12x123x^{y\ }\cdot\ 4x^{3\ }\ =\ 12x^{12}  

a)

9

b)

15

c)

-9

d)

36

39.

52  55^2\ \cdot\ 5  

a)

25225^2  

b)

120

c)

535^3  

d)

102 or 10010^2\ or\ 100  

40.

The bottom number of a power is called...

a)

Power

b)

Exponent

c)

Base

d)

The big one

41.

The little number of a power is called...

a)

Base

b)

Power

c)

Exponent

d)

The little one

42.

56y - 38y =

(a)  

43.

-19y - 23y =

(a)  

44.

32a7 - 51a7 =

a)

19a7

b)

83a7

c)

-19a7

d)

-83a7

45.
a)
10x9
b)
24x14
c)
24x9
d)
10x14
46.

Simplify: (3x4y5)2

a)

9x8y10

b)

6x8y10

c)

9x6y7

d)

6x6y7

47.
a)
8x4
b)
8x8
c)
6x4
d)
6x8
48.
Simplify the expression.
a)
9x3
b)
2x3
c)
2x4
d)
9x4
49.

Simplify the following expression: 2c3 + 8c3

a)

10c6

b)

10c9

c)

10c3

d)

10 + c3

50.
Rewrite using a positive exponent.
w-13
a)
-w13
b)
1/w13
c)
1/w-13
d)
w13
51.
Simplify y0

a)
y
b)
0
c)
1
d)
1y
52.

Simplify. Express using exponents.

a)

12x6y4

b)

12x10y6

c)

22x10y6

d)

22x6y6

53.

When dividing, I need (a)   the exponents.

54.

Evaluate the expression using the quotient rule. (subtract the exponents)

a)

x13

b)

x5

c)

x36

d)

x-5

55.
Evaluate the expression using the quotient rule.
a)
1
b)
g10
c)
g25
d)
g
56.

subtract the exponents and simplify the fraction

a)

8x4

b)

8x8

c)

6x4

d)

6x8

57.

subtract the exponents and simplify the fraction

a)

4y6

b)

4y22

c)

30y6

d)

30y22

58.

Simplify. (subtract the exponents and simplify the fraction)

a)

6r6

b)

3r4

c)

3r6

d)

6r4

59.

Simplify. (subtract the exponents and simplify the fraction)

a)

16y6

b)

9y5

c)

16y5

d)

9y6

60.

Simplify.(subtract the exponents and simplify the fraction)

a)

12x6y4

b)

12x10y6

c)

22x10y6

d)

22x6y6

61.

Simplify. (subtract the exponents and simplify the fraction)

a)

2y24

b)

210

c)

2y10

d)

2y14

62.

Simplify. (subtract the exponents and simplify the fraction)

a)

10x-2

b)

2x2

c)

2x12

d)

10x12

63.
(d4)(d5)
a)
2d4
b)
d9
c)
d2
d)
2d
64.
2a x 6a2
a)
12a3
b)
12a
c)
2a2
d)
6a3
65.
(-x5)(y3)
a)
-x8y
b)
-xy8
c)
-x5y3
d)
-(xy)8
66.
(4x)(2x2)
a)
8x
b)
6x3
c)
8x3
d)
8x2
67.
(-4x)(2y)
a)
-8xy
b)
-8xy2
c)
-4xy
d)
2xy
68.
(-4a)(3abc)
a)
-12abc
b)
-12bc
c)
-4a2bc
d)
-12a2bc
69.
Simplify (-7y2)(5y4)
a)
-35y6
b)
-2y6
c)
-35y8
d)
-2y8
70.
Simplify (-5a-3)(3a6b)
a)
-15a3b
b)
-15a9b
c)
45ab2
d)
-45a9b2
71.
(-2)³⋅(-2)⁶
a)
(-2)⁹
b)
(-2)¹⁸
c)
(-2)⁻³
d)
(-2)
72.
a)
10x9
b)
24x14
c)
24x9
d)
10x14
73.
a)
-35y6
b)
-35y5
c)
-2y6
d)
-2y5
74.
(3c2)(10c7)
a)
13c9
b)
30c5
c)
30c9
d)
-30c9
75.
-2x(x7 + 5)
a)
-8x7 - 10
b)
-2x8 - 10x
76.
-8x(x - 8)
a)
-8x2 + 64x
b)
-8x2 - 64
77.
(3c5)(12c3)
a)
15c15
b)
15c8
c)
36c15
d)
36c8
78.

Simplify (-8)-2

a)

1/-82

b)

1/82

c)

1/64

d)

-64

79.

Simplify (-8)-2

a)

1/-82

b)

1/82

c)

1/64

d)

-64

80.
Simplify 3-3
a)
-27
b)
-9
c)
-1/9
d)
1/27
81.

Simplify 5-2

a)

-10

b)

1/25

c)

1/-52

d)

-1/10

82.
3⁻⁴
a)
1 ⁄ 81
b)
-81
c)
81
d)
1 ⁄ 12
83.
y⁻¹⁰
a)
1 ⁄ y¹⁰
b)
y¹⁰
c)
-y¹⁰
d)
-1 ⁄ y¹⁰
84.
7-2
a)
49
b)
10/49
c)
-49
d)
1/49
85.
What does the expression in the picture simplify to?
a)
−9
b)
1 / 9
c)
27
d)
1 / 27
86.
Which expression is equivalent to the expression in the picture?
a)
47⋅ 44
b)
47 / 44
c)
1 / 43
d)
−43
87.
Which expression is equivalent to the expression in the picture?
a)
2822
b)
2−6
c)
24
d)
26
88.
Which expression is equivalent to (y9)−2  ?
a)
y18
b)
y11
c)
1/y18
d)
y9/2
89.
Make this negative exponent positive.
9−3
a)
93
b)
1/9−3
c)
1/93
d)
729
90.
Anything raised to a power of zero is always: 
a)
0
b)
1
c)
itself
d)
negative
91.

Simplify y0

(a)  

92.

Simplify (-9)0

(a)  

93.

What goes up and down, but always remains in the same place?

a)

Chair

b)

Stairs

c)

Car

d)

Water

94.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

95.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

96.

Simplify:

(-9)0

a)

-9

b)

-1

c)

1

d)

9

97.

Simplify:

(32)0

a)

-1

b)

1/32

c)

-1/32

d)

1

98.

Simplify:

(-8.6)0

a)

0

b)

-1

c)

1

d)

-8.6

99.

Simplify:

5-2

a)

-10

b)

1/25

c)

1/52

d)

-1/10

100.

Simplify:

4-2

a)

-1/16

b)

1/16

c)

-16

d)

16

101.

Simplify:

2-5

a)

1/16

b)

-1/32

c)

1/32

d)

1/10

102.

Simplify:

8-2

a)

-1/64

b)

1/16

c)

1/64

d)

-1/16

103.

Simplify:

3-3

a)

-1/27

b)

1/27

c)

1/9

d)

-1/9

104.

Simplify:

-(7)0

a)

-1

b)

1

c)

1/7

d)

-1/7

105.

Write this expression using positive exponent:

9-3

a)

93

b)

1/9-3

c)

1/93

d)

729

106.

Write this expression using positive exponent:

x-7

a)

-7

b)

-7x

c)

1/x7

d)

-1/x7

107.

Write this expression using a positive exponent:

g-7

a)

1/g7

b)

g7

c)

1/g-7

d)

-g7

108.

Rewrite the expression using a positive exponent:

w-13

a)

-w13

b)

1/w13

c)

1/w-13

d)

w13

109.

Rewrite the expression using a positive exponent:

7-10

a)

1/710

b)

710

c)

1/7-10

d)

-70

110.
Which is greater,  26540 or 50?
a)
26540
b)
50
c)
They are the same
d)
Zero is greater
111.

Simplify:

5x-3

a)

1/5x3

b)

1/x5

c)

-5/x3

d)

5/x3

112.

Write in simplified exponent form with no negative exponents.

184\frac{1}{8^{-4}}  

a)

184\frac{1}{8^4}  

b)

184-\frac{1}{8^4}  

c)

848^4  

d)

84-8^4  

113.

Rewrite the expression using positive exponents:

3x⁻²

a)

3 ⁄ x²

b)

1 ⁄ 3x²

c)

x² ⁄ 3

d)

-3x²

114.

Simplify:

33x-6

a)

27/x6

b)

9/x6

c)

27x6

d)

27/x-6

115.

Simplify:

7a-5b3

a)

7a5/b3

b)

b3/7a5

c)

7b3/a-5

d)

7b3 /a5

116.

Simplify:

4a-3b-2

a)

a3b2/4

b)

4a3/b2

c)

4/a3b2

d)

1/4a3b2

117.

Simplify:

8-2a-5b3

a)

b3/64a5

b)

b3/16a5

c)

a5/64b3

d)

b3/-64a5

118.

Simplify:

52x-5b-3

a)

10/x5b3

b)

25/x5b3

c)

1/25x5b3

d)

25/x-5b-3

119.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

120.

Simplify:

(-9)0

a)

-9

b)

-1

c)

1

d)

9

121.

Simplify:

(32)0

a)

-1

b)

1/32

c)

-1/32

d)

1

122.

Simplify:

(-8.6)0

a)

0

b)

-1

c)

1

d)

-8.6

123.

Simplify:

5-2

a)

-10

b)

1/25

c)

1/52

d)

-1/10

124.

Simplify:

4-2

a)

-1/16

b)

1/16

c)

-16

d)

16

125.

Simplify:

2-5

a)

1/16

b)

-1/32

c)

1/32

d)

1/10

126.

Simplify:

8-2

a)

-1/64

b)

1/16

c)

1/64

d)

-1/16

127.

Simplify:

3-3

a)

-1/27

b)

1/27

c)

1/9

d)

-1/9

128.

Simplify:

-(7)0

a)

-1

b)

1

c)

1/7

d)

-1/7

129.

Write this expression using positive exponent:

9-3

a)

93

b)

1/9-3

c)

1/93

d)

729

130.

Write this expression using positive exponent:

x-7

a)

-7

b)

-7x

c)

1/x7

d)

-1/x7

131.

Write this expression using a positive exponent:

g-7

a)

1/g7

b)

g7

c)

1/g-7

d)

-g7

132.

Rewrite the expression using a positive exponent:

w-13

a)

-w13

b)

1/w13

c)

1/w-13

d)

w13

133.

Rewrite the expression using a positive exponent:

7-10

a)

1/710

b)

710

c)

1/7-10

d)

-70

134.
Which is greater,  26540 or 50?
a)
26540
b)
50
c)
They are the same
d)
Zero is greater
135.

Simplify:

5x-3

a)

1/5x3

b)

1/x5

c)

-5/x3

d)

5/x3

136.

Write in simplified exponent form with no negative exponents.

184\frac{1}{8^{-4}}  

a)

184\frac{1}{8^4}  

b)

184-\frac{1}{8^4}  

c)

848^4  

d)

84-8^4  

137.

Rewrite the expression using positive exponents:

3x⁻²

a)

3 ⁄ x²

b)

1 ⁄ 3x²

c)

x² ⁄ 3

d)

-3x²

138.

Simplify:

33x-6

a)

27/x6

b)

9/x6

c)

27x6

d)

27/x-6

139.

Simplify:

7a-5b3

a)

7a5/b3

b)

b3/7a5

c)

7b3/a-5

d)

7b3 /a5

140.

Simplify:

4a-3b-2

a)

a3b2/4

b)

4a3/b2

c)

4/a3b2

d)

1/4a3b2

141.

Simplify:

8-2a-5b3

a)

b3/64a5

b)

b3/16a5

c)

a5/64b3

d)

b3/-64a5

142.

Simplify:

52x-5b-3

a)

10/x5b3

b)

25/x5b3

c)

1/25x5b3

d)

25/x-5b-3

143.

The half-life of Uranium is 2.5 x 105 years. What is this in standard form?

a)

2500000

b)

250

c)

25000

d)

250000

144.

Write 4.83 x 10-6 in Standard Form.

a)

0.00048300

b)

0.00004830

c)

0.00000483

d)

0.00000438

145.

Convert 0.0000037 to Scientific Notation.

a)

.37 x 10-7

b)

3.7 x 10-6

c)

37 x 10-5

d)

370 x 10-4

146.

Mercury’s average distance from the sun is 57,190,000 km. What is the distance in scientific notation?

a)

5719 x 104

b)

571.9 x 105

c)

57.19 x 106

d)

5.719 x 107

147.

(3 x 107)(3.1 x 10-4)

a)

9.3 x 10-28

b)

9.3 x 103

c)

6.1 x 103

d)

6.1 x 10-28

148.
a)

2.1 x 106

b)

2.1 x 10-6

c)

9.9 x 106

d)

9.9 x 10-6

149.

The thickness of a human hair can be about 6 x 10-3 centimeters. Which shows this thickness in standard form?

a)

6000 cm

b)

0.06 cm

c)

0.006 cm

d)

0.0006 cm

150.

The speed of light is about 300 million meters per second. Which expression shows this speed in scientific notation?

a)

300 x 106

b)

300 x 10-6

c)

3 x 108

d)

3 x 10-8

151.

To travel from Earth to Saturn, the craft needs to travel a total distance of 1.4 x 109 km. A spacecraft leaves Earth’s orbit at a speed of 7 x 105 km per day. How long will it take the spacecraft to reach Saturn? Express your answer in correct scientific notation.

a)

2 x 104

b)

0.2 x 104

c)

2 x 103

d)

0.7 x 104

152.

There are approximately 3.1 x 108 people in the United States. If on average each person has 4.1 x 101 coins lying around on dressers, in pockets, in cars, etc., how many total coins do all the people in the U.S. have?

a)

127.1 x 108

b)

12.71 x 109

c)

1.271 x 1010

d)

.1271 x 1011

153.

There are approximately 3.61 x105 babies born every day. How many babies are born in 30 days? Choose all that are correct.

a)

10830000

b)

10.83 x 106

c)

1.083 x 107

d)

.1083 x 108

154.

The average distance from Jupiter to the Sun is about 5 x 108 miles. The average distance from Venus to the Sun is about 7 x 107 miles. Which planet is further from the Sun?

a)

Venus

b)

Earth

c)

Mars

d)

Jupiter

e)

Saturn

155.
How would you write 564,000,000 in scientific notation?
a)
5.64 x 10-7
b)
5.64 x 106
c)
5.64 x 108
d)
56.4 x 107
156.
When writing a number in scientific notation, the first number must be greater than 1, but less than 10.
a)
False
b)
True
157.
How do you write
1001
in scientific notation?
a)
1.0001 x 104
b)
1.01 x 105
c)
1.001 x 103
d)
10.1 x 103
158.
Express the following in scientific notation:
.000457
a)
457 x 106
b)
457 x 10-6
c)
4.57 x104
d)
4.57 x 10-4
159.
What is scientific notation?
a)
A long way to write really short  numbers
b)
A short way to write really long numbers
c)
I don't know...
d)
None of the above
160.
UNDERSTANDING
If the exponent is a positive number...
a)
you will get a large number
b)
you will get a smaller number
161.
UNDERSTANDING
If the exponent is a negative number...
a)
you will get a large number
b)
you will get a small number
162.
When your exponent is negative, you move your decimal....
a)
to the right
b)
to the left
c)
to both sides
d)
nowhere.... the decimal goes nowhere
163.
Which of the following is correct scientific notation?
a)
20.35 x 104
b)
.2035 x 104
c)
2035 4
d)
2.035 x104
164.
What is 7.0 x 10-5 in standard form? 
a)
.0007
b)
.00007
c)
.000007
d)
.0000007
165.
How do you write
8.317 x 106
in standard form?
a)
8, 371, 000
b)
83, 170, 000
c)
837, 100
d)
8, 317, 000
166.
Put the following in scientific notation:
23,948
a)
23.948 x 103
b)
2.3948 x 104
c)
2.3948 x 10-4
d)
0.23948 x 105
167.

Convert the following number to scientific notation: 43,000,000

a)

43x10⁶

b)

4.3×10⁷

c)

430×10⁵

d)

4.3×10⁻⁷

168.
Convert the following number to scientific notation:
12,000,000
a)
1.2 x 107
b)
1.2 x 106
c)
12 x 107
169.
Convert the following number to scientific notation:
345,000
a)
3.45 x 103
b)
3.45 x 106
c)
3.45 x 105
170.

Convert the following number to scientific notation: 520,000,000

a)

52 x 107

b)

5.2 x 107

c)

5.2 x 108

d)

0.52 x 109

171.
Scientific Notation is made up of two number parts. The first part should be a number between 1 and 100.
a)
True
b)
False
172.

Convert the following number to scientific notation: .000457

a)

457 x 106

b)

457 x 10-6

c)

4.57 x104

d)

4.57 x 10-4

173.
True or False:  The following is written in scientific notation:  13.5 x 108
a)
TRUE 
b)
 FALSE
174.
Which one of these numbers is in scientific notation?
a)
8.987000
b)
8.98 x 106
c)
80.987 x 10
d)
8.986
175.
The first term in scientific notation must be _________.
a)
greater than 0 and less than 10
b)
greater than or equal to 1 and smaller than 10
c)
greater than 1 and less than 9
d)
greater than 0 and less than 9
176.

True or False: Scientific notation is made up of two number parts. The second part is a power of 10.

a)

True

b)

False

177.

If the exponent is a positive number the original number was...

a)

a really big number.

b)

a really small number.

178.

If the exponent is a negative number the original number was...

a)

a really large number.

b)

a really small number.

179.
Write 0.00000707 in scientific notation.
a)
7.07 x 10-6
b)
7.07 x 106
c)
707 x 108
d)
707 x 10-8
180.
Express the following in scientific notation:
.000457
a)
457 x 106
b)
457 x 10-6
c)
4.57 x104
d)
4.57 x 10-4
181.
Try to change the number back to standard form: 3.97  x  10-2
a)
0.000397
b)
0.0397
c)
0.0000397
d)
0.397
182.
Try to change the number back to standard form:  6.79  x  104
a)
679,000
b)
6,790
c)
67,900
d)
6,790,000
183.
Convert the following number to standard form:
4.2 x 104
a)
420,000
b)
42,000
c)
0.000 42
d)
4,200
184.
Convert the following number to standard form:
8.15 x 106
a)
815,000
b)
815,000,000
c)
8,150,000
d)
0.00000815