Free Printable Exponents

1.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

2.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

3.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

4.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

5.

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

6.

Simplify 4^-2=

a)

1/16

b)

-16

c)

1/4

d)

-42

7.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

8.

x^-3

a)

-x³

b)

1 / x³

c)

1 / x^-3

d)

-x^-3

9.

a)

b)

c)

d)

10.

a)

b)

c)

d)

11.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

12.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

13.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

14.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

15.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

16.

Simplify

a)

x⁴/3

b)

3x¹⁰

c)

36x¹⁰

d)

3x⁴

17.

a)

2 / x²

b)

-2x²

c)

2x²

d)

2x¹⁴

18.

Simplify
x³⋅x²

a)

x⁶

b)

x⁵

c)

x

d)

x⁴

19.

Simplify
x⁴⋅x³⋅x

a)

x⁸

b)

x¹²

c)

x⁷

d)

x¹⁰

20.

Simplify
(x²)³

a)

x³

b)

x⁵

c)

x⁶

d)

x⁴

21.

Simplify
y⁸⋅y³

a)

y²⁴

b)

y¹¹

c)

y⁵

d)

y¹⁵

22.

Expand
(xy)³

a)

x⋅x⋅x⋅y

b)

xy⋅xy⋅xy

c)

x⋅y⋅y⋅y

d)

3x⋅3y

23.

Simplify

a)

y²

b)

y³⁵

c)

y¹²

d)

y¹⁴

24.

Simplify
(y³)⁴

a)

y⁷

b)

y¹²

c)

y^-1

d)

y⁸

25.

Simplify

a)

x¹²

b)

x¹⁷

c)

x⁶

d)

x²³

26.

Simplify

a)

z

b)

z¹²

c)

1

d)

z¹⁴

27.

Expand
x⁵

a)

x

b)

x⋅x⋅x

c)

x⋅x⋅x⋅x⋅x

d)

x⋅x

28.

Simplify

a)

z¹⁵

b)

z⁸

c)

z³

d)

z¹¹

29.

Simplify

a)

1

b)

x²

c)

x¹⁸

d)

x¹¹

30.

Simplify

a)

x⁴

b)

x⁶

c)

x²⁹

d)

x²⁰

31.

Expand
z⁴

a)

z

b)

z⋅z

c)

z⋅z⋅z

d)

z⋅z⋅z⋅z

32.

Expand fully.
(x²)³

a)

x⋅x⋅x

b)

x²⋅x²⋅x²

c)

x⋅x⋅x⋅x⋅x⋅x

d)

x⋅x⋅x⋅x⋅x

33.

Simplify
(z⁴)³⋅z⁴

a)

z¹¹

b)

z¹⁶

c)

z⁵

d)

z²⁸

34.

(xy)³⋅x²⋅y⁵

a)

x⁸y⁵

b)

x³y⁶

c)

x⁵y⁸

d)

x⁶y⁵

35.

Simplify

a)

75x⁶

b)

3x²

c)

75x²

d)

20x⁶

36.

Simplify

a)

x⁴/3

b)

3x¹⁰

c)

36x¹⁰

d)

3x⁴

37.

Simplify

a)

w²⁴y⁹

b)

w¹¹y⁶

c)

y³/w⁶

d)

w⁶/y³

38.

How do you write 2 x 2 x 2 x 2 with an exponent?

a)

4²

b)

2⁴

c)

2²

39.

A scientist reports that a bacteria culture contains 3⁴ bacteria.
How many bacteria is that?

a)

12

b)

81

c)

7

d)

95

40.

Which one shows the numbers in order from biggest to smallest?

a)

3²,2³,6¹

b)

6¹,2³,3²

c)

2²,6¹,3²

41.

3⁴is bigger than 4³.

a)

True

b)

False

42.

Any number written to the 0 power is always 1
Example: 8⁰=1

a)

True

b)

False

43.

To square a number is to use what mathematical operation?

a)

Division

b)

Subtraction

c)

Multiplication

d)

Addition

44.

Find the equivalent expression.

9 x 9 x 9 x 9 x 9

a)

9⁵

b)

9¹⁵

c)

9 x 5

d)

9 + 9 + 9 + 9+ 9

45.

5⁴=

a)

20

b)

625

c)

1024

46.

To square a number is to use what mathematical operation?

a)

Division

b)

Subtraction

c)

Multiplication

d)

Addition

47.

The exponent equivalent of 20 x 20 x 20 is

a)

20 x 3

b)

20³

c)

3²⁰

48.

What is the number in a power that tells how many times the base is used as a factor?

a)

Expression

b)

Exponent

c)

Factor

d)

Term

49.

Choose the answer.
5²

a)

10

b)

15

c)

20

d)

25

50.

What operation do you use with exponents?

a)

addition

b)

subtraction

c)

multiplication

d)

division

51.

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

a)

4

b)

2

c)

16

d)

not here

52.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

d)

not here

53.

How do you write 2 x 2 x 2 x 2 with an exponent?

a)

4²

b)

2⁴

c)

2²

54.

Any number written to the 0 power is always 1
Example: 8⁰=1

a)

True

b)

False

55.

Which is larger?

1⁵ or 1⁸

a)

1⁵

b)

1⁸

c)

They are equal

56.

5⁴=

a)

20

b)

625

c)

1024

57.

What is 3³?

a)

6

b)

9

c)

27

d)

54

58.

Which is equivalent to $\left(\frac{1}{2}\right)^3$

a)

$\frac{1}{6}$

b)

$\frac{3}{6}$

c)

$\frac{1}{8}$

d)

$1\frac{1}{2}$

59.

Which is equivalent to 5 x 5 x 5 x 5

a)

5³

b)

5⁴

c)

4⁵

d)

5⁵

60.

The exponent equivalent of 20 x 20 x 20 is:

a)

20 x 3

b)

20³

c)

3²⁰

d)

2000

61.

Which is equivalent to 4 x 4 x 4 x 4 x 4

a)

4⁶

b)

5⁴

c)

4⁴

d)

4⁵

62.

Which is equivalent to (5.2)²

a)

10.4

b)

2704

c)

27.04

d)

270.4

63.

Math class is my favorite

a)

Yes

b)

No

64.

7⁰ = ?

a)

1

b)

7

c)

0

d)

-7

65.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

66.

56¹= ?

a)

56

b)

0

c)

1

d)

65

67.

56¹= ?

a)

56

b)

0

c)

1

d)

65

68.

Which is equivalent to 2⁴

a)

8

b)

20

c)

16

d)

12

69.

Which is equivalent to 4 x 4 x 4 x 4 x 4

a)

4⁶

b)

5⁴

c)

4⁴

d)

4⁵

70.

Choose the answer.
5^{2 = ?}

a)

10

b)

15

c)

20

d)

25

71.

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

a)

4

b)

2

c)

16

d)

not here

72.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

d)

not here

73.

The exponent equivalent of 20 x 20 x 20 is:

a)

20 x 3

b)

20³

c)

3²⁰

d)

2000

74.

What is the value of 100⁰?

a)

1

b)

0

c)

100

d)

not here

75.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

76.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

77.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

78.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

79.

Is the pictured graph growth, decay, or linear or none?

a)

Growth

b)

Decay

c)

Linear

d)

None

80.

Is the pictured graph growth, decay, or linear or none?

a)

Growth

b)

Decay

c)

Linear

d)

None

81.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

82.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

83.

The growth factor for this table is

a)

2

b)

4

c)

12

d)

144

84.

The growth factor for this table is

a)

2

b)

4

c)

12

d)

144

85.

The equation for this table is

a)

y = 1(2^x)

b)

y = 1(12^x)

c)

y = 12x

d)

y = 12x + 1

86.

The equation for this table is

a)

y = 3x + 50

b)

y = 50^x

c)

y = 3^x

d)

y = 50(3^x)

87.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

88.

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^twhere t is the number of years since 1990. What was the population in 1990?

a)

0 people

b)

It doesn't say

c)

I don't know

d)

6191

89.

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What percent did the population increase each year?

a)

4%

b)

It doesn't say

c)

I don't know

d)

400%

90.

Solve 8 = 2^5x+7

a)

⅘

b)

¼

c)

-⅘

d)

-¼

91.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

92.

Solve 3³ = 3^{4x + 2}

a)

¼

b)

-¼

c)

½

d)

-½

93.

Solve for n:
2^-2n = 2⁶

a)

-1

b)

-7

c)

5

d)

-3

94.

Solve for b:
4^{3b - 3} = 1/16

a)

7

b)

-1/4

c)

1/2

d)

1/3

95.

Solve for r:
3^-3r = 3⁵

a)

-4

b)

-5/3

c)

2

d)

8

96.

Solve for x:
3^2x = 27

a)

3/2

b)

-2

c)

0

d)

5

97.

Solve for p:
4^p+2 = 64

a)

-16/9

b)

1

c)

8

d)

7/6

98.

Solve for a:
5^{a + 2} = 1/125

a)

-1

b)

-6/7

c)

-5

d)

4

99.

Solve for x:
(-3)^x = (-3)¹³

a)

13

b)

-3

c)

x + 13

d)

x -13

100.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

101.

Solve for x:
5^2x = 5^-x

a)

0

b)

-6

c)

8

d)

1

102.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

103.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

104.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

105.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

106.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

107.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

108.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

109.

Solve for a:
5^{a + 2} = 1/125

a)

-1

b)

-6/7

c)

-5

d)

4

110.

Solve the following exponential equation:
$9^{8-x}=27^{x-3}$

a)

$x=5$

b)

$x=-5$

c)

$x=\frac{1}{5}$

d)

$x=-\frac{1}{5}$

111.

Solve the following exponential equation:

7^{-x}=49

a)

$x=1$

b)

$x=-1$

c)

$x=2$

d)

$x=-2$

112.

Solve the following exponential equation:
$8=2^{5x+7}$

a)

$x=\frac{4}{5}$

b)

$x=\frac{1}{4}$

c)

$x=-\frac{4}{5}$

d)

$x=-\frac{1}{4}$

113.

How would you solve an exponential equation like the one below:

36=6^x

a)

Rewrite $36$ as $6^2$

b)

Set the exponents equal to each other

c)

Rewrite $36$ as $6^3$

d)

Multiply the exponents

114.

Solve the following exponential equation:

\left(\frac{1}{3}\right)^{x-1}=27

a)

$x=2$

b)

$x=-4$

c)

$x=-2$

d)

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

115.

Solve the following exponential equation:
$\left(\frac{1}{2}\right)^{2x}=4^3$

a)

$x=3$

b)

$x=-\frac{5}{2}$

c)

$x=-3$

d)

$x=\frac{5}{2}$

116.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

117.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

118.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

119.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

120.

Is this exponential growth or decay?

a)

Growth

b)

Decay

121.

Does the graph represent an exponential growth or an exponential decay function?

a)

Exponential Growth

b)

Exponential Decay

122.

What does the y-intercept of the graph represent?

a)

The amount of grams the material is gaining.

b)

The amount of grams the material is losing.

c)

The amount of grams remaining after so many years.

d)

The initial amount of grams.

123.

Which of the following is an increasing exponential function whose y-intercept is 50?

a)

y = 50(.05)^x

b)

y = 50x - 4

c)

y = (2)^x + 50

d)

y = 50(1.4)^x

124.

The amount of ants in a colony, f, that is decaying can be modeled by f(x) = 800(.87)^x, where x is the number of days since the decay started. Suppose f(20) = 49. Which of the following is true?

a)

After 20 days, there are 49 ants in the colony.

b)

After 49 days there are 20 ants in the colony.

c)

The amount of ants times 20 is 49.

d)

After 20 days the amount of ants remaining decreases by 49.

125.

The amount of downloads for an album on iTunes, g(d), where d is the number of days since the album was first uploaded can be represented as
g(d) = 5^1.5d
How many downloads will the album have after 3 days?

a)

125

b)

11

c)

1398

d)

140

126.

A collectible car has been going up in price by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?

a)

$0.29

b)

$2,900,000,000

c)

$46,704.79

d)

$145,000

127.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?

a)

Increasing

b)

Decreasing

128.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 12 represent?

a)

The predicted increase in number of elephants in the refuge each year.

b)

The predicted decrease in number of elephants in the refuge each year.

c)

The number of years it will take for the elephant population to stop increasing.

d)

The initial amount of elephants in the park.

129.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 1.015 represent?

a)

The number of elephants was 1,015 in 1975.

b)

The number of elephants increases by 1.5% each year.

c)

The number of elephants increases by 101.5% each year.

d)

The number of elephants is multiplied by 1.015 each year.

130.

The amount of ibuprofen (medicine for headaches) breaks down by 30% each hour. If a person took a 200 milligram ibuprofen, how much will be left after 3 hours?

a)

5.4 mg

b)

68.6 mg

c)

.0054 mg

d)

2,400,000 mg

131.

Simplify the expression x(3x)²

a)

3x²

b)

9x²

c)

3x² + x

d)

9x³

132.

Is the graph exponential growth or decay?

a)

Exponential growth

b)

Exponential decay

133.

Is the following function exponential growth, exponential decay, linear, or none of the above.
g(x) = 740(.001)^3x

a)

Exponential growth

b)

Exponential decay

c)

Linear

d)

None of the above

134.

Is the following function exponential growth, exponential decay, linear, or none of the above?
p(x) = 13x - 5

a)

Exponential growth

b)

Exponential decay

c)

Linear

d)

None of the above

135.

Is this exponential growth or decay?

a)

Growth

b)

Decay

136.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

137.

Is this exponential growth or decay?

a)

Growth

b)

Decay

138.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

139.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

140.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

141.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

142.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

143.

Is y = -5(4)^x growth or decay?

a)

Growth

b)

Decay

144.

What is the range of y=2^x+1-3?

a)

(-∞,∞)

b)

(-3, ∞)

c)

(-1, ∞)

d)

(-∞, -3)

145.

Is y = 54(.20)^x growth or decay?

a)

Growth

b)

Decay

146.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the value after 7 years?

a)

$800

b)

$8367.70

c)

$6600

d)

$25,707.36

Exponents

Total questions: 146

Worksheet time: 1hrs 13mins

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