Free Printable Exponents

1.

Which is equivalent to 2⁴

a)

8

b)

20

c)

16

d)

12

2.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

d)

not here

3.

Solve 3^-3

a)

-27

b)

-9

c)

-1/9

d)

1/27

4.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

5.

$x^{9\ }\div x^5=$

a)

$x^4$

b)

$x^{14}$

c)

$x^{\frac{9}{5}}$

d)

$x^{95}$

6.

$x^{5\ }\times x^9=$

a)

$x^{45}$

b)

$x^{14}$

c)

$x^{-4}$

d)

$x^{59}$

7.

$\left(x^5\times y^{\ 2}\right)^3$

a)

$x^{15}\times y^6$

b)

$x^8\times y^5$

c)

$xy^{21}$

d)

$x^{95}$

8.

Simplify:

(5ab²)²

a)

25a²b⁴

b)

10a²b⁴

c)

5a²b⁴

d)

25ab²

9.

Simplify: (3x²)³

a)

27x⁶

b)

9x⁶

c)

3x⁶

d)

9x⁵

10.

If (2^x)⁵=2¹⁵, what does x equal?

a)

x = 3

b)

x = 5

c)

x = 10

11.

Which of the following is the correct way to simplify this expression?
$\left(\frac{a^m}{b^n}\right)^p$

a)

$\frac{a^{m\cdot p}}{b^{n\cdot p}}$

b)

$\frac{a^m+a^p}{b^n+b^p}$

c)

$a^{m\cdot p}\ b^{n\cdot p}$

12.

Simplify the following:
$\left(\frac{x^2y}{z^3}\right)^5$

a)

$\frac{x^{10}y^5}{z^{15}}$

b)

$\frac{x^{10}y}{z^{15}}$

c)

$\frac{x^{10}y}{z^3}$

13.

Simplify the following:
$\left(\frac{3x^3}{5y}\right)^2$

a)

$\frac{9x^6}{25y^2}$

b)

$\frac{9x^3}{25y}$

c)

$\frac{9x^6}{5y}$

14.

16 can be rewritten as...

a)

$2^3$

b)

$2^4$

c)

$2^5$

d)

$2^8$

15.

$\frac{1}{9}$ can be rewritten as...

a)

$3^{-3}$

b)

$-3^2$

c)

$3^{-2}$

d)

$3^9$

16.

16 and 32 both can be changed to have a base of...

a)

6

b)

4

c)

3

d)

2

17.

25 and $\frac{1}{125}$ both can be changed to have a base of...

a)

6

b)

4

c)

5

d)

2

18.

What number is the exponent?

a)

3

b)

5

c)

15

d)

125

19.

What is the value of the power?

a)

3

b)

5

c)

15

d)

125

20.

Identify the statement with the correct symbol.

a)

$5^2<2^5$

b)

$5^2>2^5$

c)

$5^2=2^5$

21.

Select ALL of the following that are equivalent to 5×5×5

a)

five cubed

b)

five squared

c)

5³

d)

3⁵

e)

125

22.

Evaluate 12 to the second power

a)

12

b)

24

c)

144

d)

122

23.

How do you say 3³ in words?

a)

Three squared

b)

Three cubed

24.

How do you say 4² in words?

a)

Four squared

b)

Four cubed

25.

Rewrite using a positive exponent.
g^-7

a)

¹/_g⁷

b)

g⁷

c)

¹/_g^-7

d)

-g⁷

26.

Find the missing exponent. $\left(6^5\right)^x=6^{-15}$

a)

-20

b)

10

c)

-3

d)

3

27.

For the expression (b^m)^{n}, which of the following is correct?

a)

A. b^{m+n}

b)

B. b^{mn}

c)

C. b^{m-n}

d)

D. 1 / b^n

28.

Is the equation TRUE or FALSE?

$\left(7^2\cdot\ 7^4\right)^5=7^{30}$

a)

TRUE

b)

FALSE

29.

Which expression is NOT equivalent to: $\left(5^{2x}\right)^3$ ?

a)

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

b)

$\left(5^{3x}\right)^2$

c)

$\left(5^5\right)^x$

d)

$\left(5^2\right)^{3x}$

30.

Which expression is equivalent to

$\left(4^3\right)^2\cdot4^{-8}$

a)

$\left(4^3\right)^2\cdot4^8$

b)

$4^5\cdot4^{-8}$

c)

$\left(\frac{1}{16}\right)$

d)

$\left(\frac{1}{4}\right)^{-2}$

31.

Any base raised to the power of zero equals

(a)

32.

$\left(2^8\right)^2$

a)

$2^{16}$

b)

$2^{10}$

c)

$2^6$

d)

$2^4$

33.

In Power of Powers property what do you do to the exponents?

a)

add

b)

subtract

c)

multiply

d)

divide

34.

True or False:

a)

True

b)

False

35.

Which is expression is equivalent to $5^3$ ? Select each correct expression.

a)

$5^7\cdot5^{-4}$

b)

$\frac{5^{12}}{5^4}$

c)

$5+5^2$

d)

$5^0\cdot5^3$

e)

$5^3-5^0$

36.

When the bases are being divided, you multiply the exponents.

a)

TRUE

b)

FALSE

37.

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

a)

add

b)

subtract

c)

multiply

d)

divide

38.

When a power is raised to a power, you must _______________________

a)

divide the exponets

b)

multiply the exponents

c)

add the exponets

d)

subtract the exponents

39.

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

a)

add

b)

subtract

c)

multiply

d)

divide

40.

Which of the following represents the value of any number raised to the power of 0?

a)

0

b)

1

c)

The number itself

d)

Undefined

41.

Rewrite the expression using a rational exponent:

a)

$x^{\frac{7}{4}}$

b)

$x^{\frac{4}{7}}$

c)

$x^{\frac{1}{7}}$

d)

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

42.

What is 7¹?

a)

1

b)

7

c)

0

d)

14

43.

Which of the following is correct?

a)

$\frac{Power}{Root}$

b)

$\frac{Root}{Power}$

44.

We do not have to write the index if it is

a)

2

b)

1

c)

3

d)

0

45.

For the rational exponent expression $25^{\frac{1}{2}}$ select all equivalent expressions

a)

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

b)

$5$

c)

$\sqrt[]{25}$

d)

$\sqrt[2]{5^2}$

46.

Write in exponential form
√x⁵

a)

X¹∕ ⁵

b)

X ²⁄⁵

c)

X⁵⁄ ²

d)

X⁵

47.

Simply the expression. $e^{-4}\cdot e^6$

a)

$e^{-2}$

b)

$\frac{1}{e^2}$

c)

$e^2$

d)

$e^{24}$

e)

$e^{-24}$

48.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

49.

Simplify $\left(2^5\right)^4$ . Write your answer using only positive exponents.

a)

$2^1$

b)

$2^9$

c)

$2^{20}$

d)

$2^{22}$

50.

What is the value of x?
3^{16 =}(3⁸)(3^x)

a)

2

b)

8

c)

4

d)

1

51.

Find the missing exponent: $\left(5d^4\right)^?=625d^{16}$

a)

4

b)

12

c)

20

d)

None of the above

52.

$y^5\cdot y^9\cdot y^2$

a)

$16y$

b)

$y^{16}$

c)

$12y$

d)

$y^{12}$

53.

Evaluate: 6^-3 ÷ 6³

a)

6^-6

b)

6⁰

54.

The value of 2^-3 = -8

a)

True

b)

False

55.

What does 8^-2 equal?

a)

1/16

b)

1/64

c)

-16

d)

-64

56.

Rewrite using a positive exponent.
(-5)^-4

a)

(-5)⁴

b)

¹/_(-5)^-4

c)

¹/_(-5)⁴

d)

-625

57.

Rewrite using a positive exponent. $-5x^{-4}$

a)

$-20x$

b)

$\frac{1}{-5x^{-4}}$

c)

$\frac{1}{-5x^4}$

d)

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

58.

Which of the following values is equivalent to $5^{-3}$

a)

$\frac{1}{15}$

b)

$\frac{1}{125}$

c)

-15

d)

-125

59.

Simplify: $2x^{-3}y$

a)

$\frac{2y}{x^3}$

b)

$\frac{y}{8x^3}$

c)

$\frac{y}{2x^3}$

d)

$-\frac{2y}{x^3}$

60.

Simplify

3^-3

a)

27

b)

-9

c)

-1/9

d)

1/27

61.

Write the following in standard form:
10^-4

a)

10,000

b)

1000

c)

.0001

d)

.000001

62.

Simplify: $3x^{-2}$

a)

$\frac{3}{x^2}$

b)

$-3x^2$

c)

$\frac{1}{3x^2}$

d)

$\frac{-3}{x^2}$

Exponents

Total questions: 62

Worksheet time: 2hrs 12mins

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