Free Printable Exponents and roots

1.

9²= ?

a)

18

b)

92

c)

81

d)

3

2.

4²= ?

a)

16

b)

8

c)

42

d)

2

3.

$\left(\frac{4}{8}\right)^2$ = ?

a)

$\frac{8}{16}$

b)

$\frac{16}{8}$

c)

$\frac{16}{64}$

4.

2³= ?

a)

8

b)

6

c)

16

d)

4

5.

4³= ?

a)

64

b)

12

c)

16

d)

43

6.

$\sqrt{36\ }\ =\ ?$

a)

4

b)

6

c)

18

d)

12

7.

x²= 100. What does x equal?

a)

9

b)

10

c)

20

d)

9

8.

What is the square root of 49?

a)

6

b)

7

c)

8

d)

9

9.

What is the cube root of 8?

a)

8

b)

2

c)

3

d)

4

10.

x³= 27. What is x equal to?

a)

3

b)

4

c)

5

d)

5.2

11.

What is the cube root of 1000?

a)

100

b)

10

c)

9

d)

1

12.

x³ = 216. x =?

a)

14

b)

12

c)

6

d)

4

13.

x² = 169

a)

x = 13

b)

x = 16

c)

x = 14

d)

x = 3

14.

What is the cube root of 125?

a)

15

b)

5

c)

25

d)

35

15.

Which of the following is equivalent to 3³

a)

27

b)

3 x 3 x 3

c)

3 x 9

d)

All of the above

16.

Simplify $5x^3\ •\ 2x^2$

a)

10x⁵

b)

3x

c)

10x⁶

d)

7x⁵

17.

Simplify

$\left(\frac{x}{y}\right)^7$

a)

$\left(\frac{x^7}{y}\right)$

b)

$\left(\frac{x}{y^7}\right)$

c)

$\left(\frac{x^7}{y^7}\right)$

d)

$\left(\frac{7x}{7y}\right)$

18.

Simplify the following expression: $\left(3^{-2}\right)^3$

a)

$\frac{1}{3^6}$

b)

$3^{-6}$

c)

$\frac{1}{3^{-6}}$

d)

$3^{-5}$

19.

Match the following

a)

$x^3x^4$

1.

x⁷

b)

$\left(x^3\right)^4$

2.

x¹²

c)

$\left(xy\right)^4$

3.

x⁴y⁴

d)

$\frac{x^6}{x^4}$

4.

x²

20.

Match the following

a)

$\left(\frac{x}{y}\right)^3$

1.

x³/y³

b)

$\frac{1}{x^3}$

2.

x^-3

c)

$x^0$

3.

1

21.

Simplify the expression shown. Your answer should contain only positive exponents.

a)

b)

c)

d)

22.

a)

b)

c)

d)

23.

Simplify:
(5ab²)²

a)

25a²b⁴

b)

10a²b⁴

c)

10ab⁴

d)

25ab⁴

24.

a)

3x⁻¹y⁻⁵

b)

3x²y

c)

3xy⁵

d)

−3x³y⁷

25.

(x⁸)(x^-5)

a)

x^-40

b)

x^-13

c)

x¹³

d)

x³

26.

a)

2 / x²

b)

-2x²

c)

2x²

d)

2x¹⁴

27.

Find the missing exponent (?) in the expression below.

$\left(2z^?\right)^3=8z^{15}$

a)

2

b)

12

c)

5

d)

9

28.

Which expression is equivalent to $36x^{12}$ ?

a)

$\left(6x^3\right)^4$

b)

$12x^4\cdot3x^3$

c)

$3x^3\cdot\left(4x^3\right)^3$

d)

$\left(6x^5\right)^2\cdot x^2$

29.

Simplify the expression using exponential notation:

$a^6b^7\cdot a^4b^6$

a)

$a^{24}b^{42}$

b)

$a^{10}b^{13}$

c)

$a^{13}b^{10}$

d)

$a^3b$

30.

Evaluate ∛1

(a)

31.

Evaluate ∛512

(a)

32.

Evaluate ∛729

(a)

33.

$-\sqrt{144}$

a)

12

b)

-12

c)

-72

d)

none of the above (imaginary number)

34.

A cube with side length s has a volume of 64 cubic units. What is the length of one side?

a)

4

b)

8

c)

16

d)

32

35.

The area of a square painting is 81 cm². What is the side length of the painting?

a)

40.5 cm

b)

162 cm

c)

6,561 cm

d)

9 cm

36.

Evaluate

a)

3

b)

62

c)

6

d)

2

37.

∛125

a)

5

b)

4

c)

6

d)

7

38.

∛216

a)

6

b)

72

c)

108

d)

4

39.

∛8

a)

2

b)

4

c)

1

d)

64

40.

∛1000

a)

10

b)

9

c)

8

d)

11

41.

9²= ?

a)

18

b)

92

c)

81

d)

3

42.

2³= ?

a)

8

b)

6

c)

16

d)

4

43.

4³= ?

a)

64

b)

12

c)

16

d)

43

44.

$\sqrt{36\ }\ =\ ?$

a)

4

b)

6

c)

18

d)

12

45.

x²= 100. What does x equal?

a)

9

b)

10

c)

20

d)

9

46.

What is the cube root of 8?

a)

8

b)

2

c)

3

d)

4

47.

What is the square root of 49?

a)

6

b)

7

c)

8

d)

9

48.

x³= 27. What is x equal to?

a)

3

b)

4

c)

5

d)

5.2

49.

What is the cube root of 1000?

a)

100

b)

10

c)

9

d)

1

50.

x³ = 216. x =?

a)

14

b)

12

c)

6

d)

4

51.

Which of the following is equivalent to 3³

a)

27

b)

3 x 3 x 3

c)

3 x 9

d)

All of the above

52.

Which of the following is in exponential form?

a)

5 x 5 x 5

b)

125

c)

5³

53.

Which of the following is in standard form?

a)

25

b)

5²

c)

5 X 5

54.

Write $7^5$ in expanded form

a)

7 x 2

b)

7x 7 x 7 x 7 x 7

c)

526

d)

35

55.

$10^2$ Identify the base

a)

10

b)

2

56.

√100

a)

15

b)

10

c)

11

d)

12

57.

What is the cube root of 64?

a)

4

b)

2

c)

8

d)

-4

58.

If $\sqrt{x}=12$ what does x equal to?

a)

121

b)

124

c)

144

d)

196

59.

What is the exponent form for

6?

a)

6⁰

b)

6¹

60.

Simplify and solve: 3³ - 2³=

a)

27 - 8

b)

19

c)

20

d)

35

61.

Which is GREATER?
2⁷ or 7²

a)

2⁷

b)

7²

c)

Neither, they are equal

62.

2⁵ is the same as 2 x 5.

a)

True

b)

False

63.

What is 10⁰equivalent to?

a)

1

b)

10

c)

0

d)

100

64.

b²=361
b=...

a)

19

b)

20

c)

16

d)

17

65.

Is 225 a perfect square?

a)

Yes

b)

No

66.

The √20 is between which two integers?

a)

2 & 3

b)

3 & 4

c)

4 & 5

d)

5 & 6

67.

Estimate the square root.

a)

about 9

b)

about 10

c)

about 11

d)

about 12

68.

Which point most closely corresponds to ∛8 on the number line below? (Click the question to see the picture)

a)

P

b)

Q

c)

R

d)

S

69.

Is 225 a perfect square?

a)

Yes

b)

No

70.

True or false? 9² = 18

a)

True

b)

False

71.

$^3\sqrt{8}=$

a)

2

b)

-2

c)

±2

d)

None

72.

The number 1,000 is a...

a)

perfect square

b)

perfect cube

73.

Approximate the square root to the tenths place: √149

a)

11.9

b)

12.2

c)

74.5

d)

12.3

74.

Determine between which two numbers the cube root lies: ∛11

a)

2 and 3

b)

1 and 2

c)

3 and 4

d)

4 and 5

75.

Determine between which two numbers the cube root lies: ∛75

a)

5 and 6

b)

6 and 7

c)

3 and 4

d)

4 and 5

76.

If Madison has a square garden with an area of 256 square feet, what is the length of each of its sides?

a)

128 ft.

b)

64 ft.

c)

16 ft.

d)

32 ft.

77.

Gabriel received a cube shaped package with his Amazon order inside. The length of the side of the package was 9 inches. What was the volume of the package?

a)

27 cubic inches

b)

36 cubic inches

c)

81 cubic inches

d)

729 cubic inches

78.

Evaluate √72. Round your answer to the nearest Whole Number.

a)

7.2

b)

7

c)

8

d)

9

79.

Which points are greater than √5 ? Choose all that apply.

a)

Point M

b)

Point N

c)

Point P

d)

Point Q

e)

None of the above

80.

The √20 is between which two integers?

a)

2 & 3

b)

3 & 4

c)

4 & 5

d)

5 & 6

81.

Estimate the square root.

a)

4.2

b)

4

c)

4.6

d)

5

82.

$\sqrt{129}$

a)

11.9

b)

12.9

c)

10.4

d)

11.4

83.

The √40 is between which two consecutive whole numbers?

a)

7 & 8

b)

4 & 5

c)

5 & 6

d)

6 & 7

84.

Which of the following numbers is irrational?

a)

√8

b)

¾

c)

2

d)

-1.325

85.

What is a rational number ?

a)

A rational number is a number that cannot be written as a fraction.

b)

A rational number is a number that can be written as a ratio.

c)

A rational number cannot be a repeating decimal.

86.

a)

A, B, C

b)

B, C, A

c)

C, A, B

d)

A, C, B

87.

Given the following radical, decide if it is rational or irrational:
√16

a)

Rational

b)

Irrational

88.

4π

a)

rational

b)

irrational

89.

x³

a)

3x

b)

x * 3

c)

X * X * X

d)

0

90.

4⁰

a)

0

b)

1

c)

4

d)

-4

91.

³√64

a)

4

b)

6

c)

8

d)

9

92.

√121

a)

9

b)

10

c)

11

d)

12

93.

³√27

a)

3

b)

9

c)

4

d)

7

94.

³√1000

a)

15

b)

20

c)

100

d)

10

95.

√64

a)

6

b)

7

c)

8

d)

9

96.

³√125

a)

41.666

b)

5

c)

7

d)

3

97.

12⁰

a)

0

b)

12

c)

1

d)

-1

98.

11¹

a)

11

b)

1

c)

0

d)

111

99.

10⁴

a)

40

b)

400

c)

40000

d)

10000

100.

5³

a)

25

b)

15

c)

125

d)

150

101.

10²

a)

100

b)

20

c)

1000

d)

12

102.

3³

a)

9

b)

6

c)

36

d)

27

103.

9²

a)

18

b)

81

c)

11

d)

27

104.

12²

a)

24

b)

84

c)

144

d)

14

105.

Compare by using either <, =, or >.

$5^3$ _____ $10^2$

a)

$<$

b)

$=$

c)

$>$

106.

Compare by using either <, =, or >.

9^1

_____

1^9

a)

$<$

b)

$=$

c)

$>$

107.

Compare by using either <, =, or >.
$17^0$ ______ $2^1$

a)

$<$

b)

$=$

c)

$>$

108.

Compare by using either <, =, or >.

8^3

______

16^2

a)

$<$

b)

$=$

c)

$>$

109.

Compare by using either <, =, or >.

$2^5$ _____ $3^4$

a)

$<$

b)

$=$

c)

$>$

110.

Compare by using either <, =, or >.

$10^2$ _____ $100^1$

a)

$<$

b)

$=$

c)

$>$

111.

Compare by using either <, =, or >.

$8^2$ ______ $4^3$

a)

$<$

b)

$=$

c)

$>$

112.

Compare by using either <, =, or >.

$7^2$ _____ $3^5$

a)

$<$

b)

$=$

c)

$>$

113.

Compare by using either <, =, or >.

7² ___ 2⁶

a)

>

b)

<

c)

=

114.

Compare by using either <, =, or >.

7⁴ _____ 4⁷

a)

<

b)

>

c)

=

115.

Compare by using either <, =, or >.

2⁷ _____ 2⁶

a)

>

b)

<

c)

=

116.

Compare by using either <, =, or >.

2⁴ _____ 4²

a)

>

b)

<

c)

=

117.

Compare by using either <, =, or >.

$2^5$ _______ $6^2$

a)

$=$

b)

$>$

c)

$<$

118.

Compare by using either <, =, or >.

4³____2⁶

a)

=

b)

<

c)

>

119.

Compare by using either <, =, or >.

36 ___ 6²

a)

<

b)

>

c)

=

120.

Compare by using either <, =, or >.

45 ___ 7²

a)

=

b)

>

c)

<

121.

Compare by using either <, =, or >.

101 ___ 10²

a)

<

b)

>

c)

=

122.

Compare by using either <, =, or >.

$\sqrt{25}$ ___ 6

a)

=

b)

<

c)

>

123.

Compare by using either <, =, or >.

$\sqrt{256}$ ___ 15

a)

=

b)

<

c)

>

124.

Compare by using either <, =, or >.

$\sqrt{99}\$ ___ $\sqrt{100}$

a)

=

b)

<

c)

>

125.

Compare by using either <, =, or >.

$\sqrt{65}$ ___ 8

a)

=

b)

<

c)

>

126.

Which number is the LARGEST?

a)

2²

b)

$\sqrt{16}$

c)

5

d)

$\sqrt{26}$

127.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

e)

none of the answer choices

128.

Simplify: $6^5\cdot6^2$

a)

$6^7$

b)

$6^3$

c)

$36^7$

d)

$6^{10}$

e)

none of the answer choices

129.

Simplify: $3n^5\cdot5n^{10}$

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

e)

none of the answer choices

130.

Simplify: $\frac{2^9}{2^6}$

a)

$1^3$

b)

$0^3$

c)

$2^3$

d)

$2^{15}$

e)

none of the answer choices

131.

Simplify: $\left(3x^5\right)^6$

a)

$18x^{30}$

b)

$729x^{11}$

c)

$18x^{11}$

d)

$729x^{30}$

e)

none of the answer choices

132.

Simplify: $\left(4y\right)^{-3}$

a)

$\frac{1}{64y^3}$

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

$\frac{64}{y^3}$

e)

none of the answer choices

133.

Simplify: $\left(2m\right)^5$

a)

$10m^5$

b)

$32m^5$

c)

$25m^5$

d)

$\frac{1}{2m^5}$

e)

none of the answer choices

134.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

e)

none of the answer choices

135.

Simplify: $\frac{k^3}{5k}$

a)

$5k^2$

b)

$\frac{5}{k^2}$

c)

$\frac{k^2}{5}$

d)

$\frac{k^4}{5}$

e)

none of the answer choices

136.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

e)

none of the answer choices

137.

Simplify the expression in exponential form:
134⁰

a)

0

b)

134

c)

1

d)

none of the answer choices

138.

Evaluate

a)

$-\frac{1}{64}$

b)

$\frac{1}{16}$

c)

$\frac{1}{64}$

d)

$-\frac{1}{16}$

e)

none of the answer choices

139.

Evaluate the expression using the quotient rule.

a)

3⁴

b)

$\frac{1}{3^4}$

c)

3^-12

d)

3³²

e)

none of the answer choices

140.

Re-write the expression in radical form.
x^2/3

a)

∛x²

b)

√x³

c)

$\frac{1}{x}$

d)

∛x

e)

none of the answer choices

141.

Which TWO are equivalent to the above expression?

a)

b)

c)

d)

e)

none of the answer choices

142.

Completely Simplify:

a)

$\frac{1}{5}$

b)

$\frac{2}{10}$

c)

$\frac{2}{100}$

d)

$\frac{2}{50}$

e)

none of the answer choices

143.

a)

7²

b)

7^1/2

c)

7^-2

d)

7^-1/2

e)

none of the answer choices

144.

a)

2^3/5

b)

-2^3/5

c)

2^5/3

d)

8⁵

e)

none of the answer choices

145.

8

a)

W

b)

O

c)

R

d)

K

e)

none of the answer choices

146.

Simplify $\left(x^{\frac{1}{7}}\right)^{\frac{3}{2}}$ and write your answer in radical form.

a)

$^{21}\sqrt{x^2}$

b)

$\ ^{14}\sqrt{x^3}$

c)

$\sqrt{x^3}$

d)

$^3\sqrt{x^{14}}$

e)

none of the answer choices

147.

Simplify the expression completely and write in radical form if necessary.
(x^2/3)⁶

a)

∛x²

b)

∛x²⁰

c)

x⁴

d)

√x³

e)

none of the answer choices

148.

What is 2 cubed?

2³

a)

8

b)

6

c)

4

d)

16

149.

Which of the following is NOT a perfect square?

a)

1

b)

4

c)

100

d)

8

150.

Which of these is not a perfect square?

a)

144

b)

36

c)

121

d)

72

151.

Square roots are the opposite of ____________.

a)

Cube Roots

b)

Squaring

c)

Multiplication

d)

Absolute Value

152.

To find the square root of a number, you must divide it by 2.

a)

True

b)

False

153.

The number under the square root symbol is called the ___________.

a)

Radical

b)

Radicand

c)

Radius

d)

Radient

154.

9²= ?

a)

18

b)

92

c)

81

d)

3

155.

4²= ?

a)

16

b)

8

c)

42

d)

2

156.

$\left(\frac{4}{8}\right)^2$ = ?

a)

$\frac{8}{16}$

b)

$\frac{16}{8}$

c)

$\frac{16}{64}$

157.

4³= ?

a)

64

b)

12

c)

16

d)

43

158.

$\sqrt{36\ }\ =\ ?$

a)

4

b)

6

c)

18

d)

12

159.

x²= 100. What does x equal?

a)

9

b)

10

c)

20

d)

9

160.

What is the square root of 49?

a)

6

b)

7

c)

8

d)

9

161.

What is the exponent notation of this multiplication? $3\times3\times3=$

a)

$3^3$

b)

$3^2$

162.

$10^{5\ =}$

a)

10 x 10 x 10 x 10 x 10

b)

10 x 10 x 10 x 10

163.

$13^2\ =$

(a)

164.

What is the exponent form for
6?

a)

6⁰

b)

6¹

165.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

166.

Which number is the EXPONENT?
4^{2 =}16

a)

4

b)

2

c)

16

167.

How do you correctly say 4³

a)

4 squared

b)

3 quadrupled

c)

4 cubed

d)

4 to the power of 2

168.

What special word do you use for the exponent of 2?

a)

squared

b)

cubed

c)

triangled

d)

boxed

169.

√100

a)

15

b)

10

c)

11

d)

12

Exponents and roots

Total questions: 169

Worksheet time: 4hrs 30mins

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