Free Printable Negative and fractional Exponents

1.

Rewrite using a positive exponent.
g^-7

a)

¹/_g⁷

b)

g⁷

c)

¹/_g^-7

d)

-g⁷

2.

Rewrite each expression with a negative exponent.
¹/₁₂₅

a)

¹/_5³

b)

5³

c)

5^-3

d)

¹/_5-3

3.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

4.

Simplify (-1/2)⁰

a)

1

b)

0

c)

-1

d)

-2

5.

Simplify -4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

6.

Simplify 3^-3

a)

-27

b)

-9

c)

-1/9

d)

1/27

7.

Simplify x²y^-5

a)

x²/y⁵

b)

1/x²y⁵

c)

y⁵/x²

d)

x²/y^-5

8.

Simplify 5^-2

a)

-10

b)

1/25

c)

1/(5)²

d)

-1/10

9.

Evaluate:
8^-1

a)

1/8

b)

-8

c)

-1/8

d)

1

10.

Evaluate:
3^-2

a)

1/9

b)

-6

c)

-9

d)

-1/6

11.

What is 10^-2 written as a fraction?

a)

1/100

b)

1/1000

c)

1/10

d)

1/200

12.

4^-2 = ?

a)

2

b)

1 / 16

c)

16

d)

-8

13.

4^3/2= ?

a)

6

b)

8

c)

5.5

14.

Simplify the following expression:

a)

16

b)

32

c)

40

d)

64

15.

Write in exponential form
∛x⁷

a)

x⁷∕ ³

b)

x3⁄7

c)

3x⁷

d)

7x³

16.

a)

b)

c)

d)

17.

a)

b)

c)

d)

18.

Simplify the following expression:

a)

2

b)

4

c)

16

d)

64

19.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

20.

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

a)

(∛x)²

b)

√x³

c)

(1/x)

d)

∛x

21.

Write with positive exponents:

a)

a^-2

b)

a²

c)

1/a¹

22.

Rewrite using a positive exponent.
7^-10

a)

¹/_7¹⁰

b)

7¹⁰

c)

¹/_7^-10

d)

-70

23.

Rewrite using a positive exponent.
g^-7

a)

¹/_g⁷

b)

g⁷

c)

¹/_g^-7

d)

-g⁷

24.

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

a)

(-5)⁴

b)

¹/_(-5)^-4

c)

¹/_(-5)⁴

d)

-625

25.

Rewrite each expression with a negative exponent.
¹/₁₂₅

a)

¹/_5³

b)

5³

c)

5^-3

d)

¹/_5-3

26.

Rewrite each expression with a negative exponent.
¹/_(-5)⁷

a)

(-5)⁷

b)

¹/_(-5)^-7

c)

(-5)^-7

d)

¹/_78,125

27.

Simplify

a)

-1/6

b)

1/6

c)

6

d)

-6

28.

Simplify

a)

-1/16

b)

1/16

c)

-16

d)

16

29.

2^-1

a)

1/2

b)

1/1

c)

-1/1

d)

-1/2

30.

Solve 3^-3

a)

-27

b)

-9

c)

-1/9

d)

1/27

31.

Solve (-8)^-2

a)

1/(-8)²

b)

1/8²

c)

1/64

d)

-64

32.

Rewrite using a positive exponent.
w^-13

a)

-w¹³

b)

¹/_w¹³

c)

¹/_w^-13

d)

w¹³

33.

Simplify x^-7

a)

-7

b)

-7x

c)

1/x⁷

d)

x/7

34.

a)

49/64

b)

64/49

c)

14/16

d)

16/14

35.

Simplify the following expression:

x¹⁰ ÷ x²

a)

x⁵

b)

x¹²

c)

x⁸

d)

x²⁰

36.

How else can you write $\sqrt{x}$ ?

a)

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

b)

$x^2$

c)

$x^{-2}$

d)

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

37.

1000^⅓is the same as the cube root of 1000 =

a)

10

b)

333

c)

300

d)

100

38.

64^⅓=

a)

4

b)

8

c)

6

d)

21.3

39.

Evaluate

a)

3

b)

18

c)

9

d)

6

40.

How else could you write $4^{-2}$ ?

a)

$16$

b)

$-16$

c)

$-\frac{1}{16}$

d)

$\frac{1}{16}$

41.

4^-½=

a)

2

b)

-2

c)

½

d)

-½

42.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

43.

Which of the following is equivalent to the expression $\frac{1}{2x^7}$ ?

a)

$\left(2x\right)^{-7}$

b)

$\frac{1}{2}x^7$

c)

$\frac{1}{2}x^{-7}$

d)

$2x^{-7}$

44.

\frac{2}{x^3}=?

a)

$2x^3$

b)

$2x^{-3}$

c)

$8x^3$

d)

$8x^{-3}$

45.

Simplify fully $x^5\times x^{-2}=?$

a)

$x^3$

b)

$x^7$

c)

$x^{10}$

d)

$x^{-10}$

46.

Simplify.
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

47.

Simplify

a)

7a⁵/b³

b)

b³/7a⁵

c)

7b³/a^-⁵

d)

7b³ /a⁵

48.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

49.

a)

y⁴

b)

y⁵

c)

y⁶

d)

6^y

50.

a)

t²⁴

b)

t¹²

c)

t¹⁸

d)

t^-12

51.

a)

b)

c)

d)

52.

Write the product using exponents:

(-2) ⋅ (-2) ⋅ (-2) ⋅ (-2) ⋅ (-2)

a)

-2⁵

b)

2^-5

c)

(-2)⁵

d)

(-2)^-5

53.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

54.

Write the product using exponents: (-2) ⋅ (-2) ⋅ (-2) ⋅ x ⋅ x

a)

(-2)³ ⋅ x²

b)

-(2³ ⋅ x²)

c)

-2³ ⋅ x²

d)

8x²

55.

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

a)

(-5)⁴

b)

¹/_(-5)^-4

c)

¹/_(-5)⁴

d)

-625

56.

a)

2xy⁶

b)

8x³y⁵

c)

2x³y⁶

d)

8x³y⁶

57.

$Evaluate\ 36^{\frac{1}{2}}$

a)

6

b)

12

c)

$\sqrt{6}$

d)

$6^2$

58.

Evaluate

a)

$\frac{1}{3}$

b)

$\frac{1}{81}$

c)

$\frac{1}{19683}$

d)

$3$

59.

$Evaluate\ 6^{-2}$

a)

$\frac{1}{6^2}$

b)

$\frac{1}{36}$

c)

36

d)

$-36$

60.

$Evaluate\ \left(\frac{3}{4}\right)^{-2}$

Evaluate

a)

$-\frac{3}{4}$

b)

$-\frac{9}{16}$

c)

$\frac{3}{4}$

d)

$\frac{16}{9}$

61.

$Evaluate\ 5d^0$

a)

0

b)

5

c)

1

d)

5d

62.

Simplify

a)

$\frac{3}{4x^9}$

b)

$3x^{-9}$

c)

$3x^3$

d)

$\frac{3}{2x^6}$

63.

$Evaluate\ _3\sqrt{27a^6}$

a)

3a

b)

$3a^2$

c)

$\frac{1}{a^9}$

d)

$9a^2$

64.

$Evaluate\ \left(\frac{9v^2}{16w^4}\right)^{-\frac{1}{2}}$

a)

$\frac{3v}{4w^2}$

b)

$\frac{4w^2}{3v}$

c)

$-\frac{3v}{4w^2}$

d)

$\frac{9v}{16w^2}$

65.

-9²

a)

81

b)

-81

c)

1/81

d)

-1/81

e)

-18

66.

9^1/2

a)

4 1/2

b)

3

c)

-3

d)

1/3

e)

-1/3

67.

(-9)²

a)

81

b)

-81

c)

1/81

d)

1/3

e)

-1/81

68.

9^-2

a)

1/3

b)

-18

c)

-81

d)

1/81

e)

-1/3

69.

9^-1/2

a)

-3

b)

-4.5

c)

1/9

d)

1/3

e)

-1/3

70.

(-9)^1/2

a)

3

b)

-3

c)

4.5

d)

-4.5

e)

non-real

71.

(8)^1/3

a)

-2

b)

4

c)

8/3

d)

2

72.

1/16²

a)

256

b)

4

c)

-4

d)

1/4

e)

1/256

73.

$\left(\frac{1}{16}\right)^{-2}$

a)

-8

b)

-1/8

c)

4

d)

256

e)

1/4

74.

$\left(\frac{1}{16}\right)^{\frac{1}{2}}$

a)

1/4

b)

1/8

c)

8

d)

4

e)

-8

75.

$\frac{1}{16^{-\frac{1}{2}}}$

a)

-1/8

b)

-8

c)

-1/4

d)

4

e)

-4

76.

$\frac{1}{16^{-2}}$

a)

256

b)

1/256

c)

-1/256

d)

-32

e)

-1/32

77.

$-\left(\frac{1}{16}\right)^2$

a)

1/256

b)

-1/256

c)

1/32

d)

-1/32

e)

256

78.

$\left(-\frac{1}{16}\right)^{-2}$

a)

-256

b)

1/256

c)

-1/256

d)

256

e)

-1/32

79.

-9^-2

a)

81

b)

-81

c)

1/81

d)

-1/81

e)

-18

80.

$-\left(\frac{1}{16}\right)^{-\frac{1}{2}}$

a)

-1/8

b)

-8

c)

-1/4

d)

4

e)

-4

81.

What is 10⁰equivalent to?

a)

1

b)

10

c)

0

d)

100

82.

Simplify x^-7

a)

-7

b)

-7x

c)

1/x⁷

d)

x/7

83.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

84.

Make this negative exponent positive.
9^-3

a)

9³

b)

1/9^-3

c)

1/9³

d)

729

85.

Simplify -4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

86.

Rewrite each expression with a negative exponent.
¹/_12⁴

a)

¹/_12^-4

b)

12⁴

c)

¹/_20,736

d)

12^-4

87.

Simplify 7^-2

a)

1/49

b)

-49

c)

-14

d)

1/14

88.

What is the value of 27^⅓?

a)

27

b)

9

c)

3

d)

1/3

89.

How else can you write $\sqrt{x}$ ?

a)

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

b)

$x^2$

c)

$x^{-2}$

d)

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

90.

Choose the correct answers.

a)

A

b)

B

c)

C

d)

D

91.

Choose the correct answer.

a)

A

b)

B

c)

C

d)

D

92.

Choose the correct answer.

a)

A

b)

B

c)

C

d)

D

93.

Choose the correct answer.

a)

A

b)

B

c)

C

d)

D

94.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$7^0+8^0+9^0$

a)

3

b)

1

c)

0

d)

24

95.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$\left(\frac{3}{5}\right)^{-1}$

a)

$-\frac{5}{3}$

b)

$-\frac{3}{5}$

c)

$\frac{3}{5}$

d)

$\frac{5}{3}$

96.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$\frac{2\left(a^6b^{-6}\right)^0}{a^{-4}b^3}$

a)

$\frac{2}{a^4b^3}$

b)

$\frac{a^4}{b^3}$

c)

$\frac{b^3}{a^4}$

d)

$\frac{2a^4}{b^3}$

97.

Write the exponential expression as radical.

$27^{\frac{2}{3}}$

a)

b)

c)

d)

98.

Write the radical as exponential expression.

a)

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

b)

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

c)

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

d)

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

99.

Write the given as a radical expression and simplify.

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

a)

4

b)

2

c)

16

d)

64

100.

Evaluate the expression:

$16^{\frac{3}{4}}$

a)

8

b)

16

c)

4

d)

32

101.

Evaluate the expression:

$36^{-\frac{1}{2}}$

a)

$-6$

b)

$6$

c)

$-\frac{1}{6}$

d)

$\frac{1}{6}$

102.

Evaluate the expression:

$81^{-\frac{3}{4}}$

a)

$-27$

b)

$\frac{1}{27}$

c)

$-\frac{1}{9}$

d)

$18$

103.

Simplify the expression

\frac{w^{-5}}{w^{-8}}

a)

$w^{-3}$

b)

$w^2$

c)

$w^3$

d)

$w^{-13}$

104.

Simplify the expression

\frac{x^2y^8}{x^{-6}y^{-4}}

a)

$x^4y^4$

b)

$x^{-4}y^{12}$

c)

$x^8y^4$

d)

$x^8y^{12}$

105.

Write as a radical:

n^{\frac{1}{3}}

a)

$\sqrt{n^{\frac{1}{3}}}$

b)

$\sqrt{n^3}$

c)

d)

106.

Simplify the expression

25^{\frac{1}{2}}

a)

5

b)

10, 15

c)

12.5

d)

-5

107.

Anything to the zero power is....

x^0=?

a)

0

b)

x

c)

1

d)

Not possible

108.

Simplify the expression

125^{\frac{1}{3}}

a)

41.7

b)

11.2

c)

5

d)

62.5

109.

Simplify the expression

16^{\frac{1}{4}}

a)

4

b)

2

c)

8

d)

16

110.

Simplify the expression

4^{-\frac{1}{2}}

a)

$-\frac{1}{2}$

b)

-2

c)

2

d)

$\frac{1}{2}$

111.

$2^3$

a)

6

b)

5

c)

8

d)

-1

112.

$7^2$

a)

9

b)

14

c)

49

d)

5

113.

$2^{-1}$

a)

-2

b)

$\frac{1}{2}$

c)

D.N.E.

d)

0.2

114.

$3^{-2}$

a)

-6

b)

-9

c)

9

d)

$\frac{1}{9}$

115.

$7^{\frac{1}{3}}$

a)

$\frac{7}{3}$

b)

7.3

c)

d)

Not possible

116.

$100^0$

a)

0

b)

1

c)

10

d)

100

117.

$5^{-1}$

a)

-5

b)

$\frac{1}{5}$

c)

4

d)

0

118.

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

a)

b)

2/3

c)

8

d)

2.3

119.

$2^5$

a)

3

b)

10

c)

32

d)

16

120.

$4^{-2}$

a)

-2

b)

1

c)

$\frac{1}{16}$

d)

-8

121.

$5^{-4}$

a)

$-20$

b)

$625$

c)

$\frac{1}{625}$

d)

$\frac{1}{20}$

122.

$3^{-16}$

a)

$13$

b)

$\frac{1}{3^{16}}$

c)

$-48$

d)

$-13$

123.

$65^0$

a)

$0$

b)

$64$

c)

$\frac{1}{65}$

d)

$1$

124.

1/16^-2

a)

-8

b)

-1/8

c)

4

d)

256

e)

1/4

125.

a)

x^2/3

b)

x^3/2

c)

x³

d)

x^2.3

126.

Simplify x²y^-5

a)

x²/y⁵

b)

1/x²y⁵

c)

y⁵/x²

d)

x²/y^-5

127.

5x^1/3

a)

b)

c)

d)

128.

3x^-2y

a)

1/3x²y

b)

3/x²y

c)

3y/x²

d)

y/3x²

129.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

130.

Write in exponential form
∛x⁷

a)

x⁷∕ ³

b)

x3⁄7

c)

3x⁷

d)

7x³

131.

Write in exponential form
√x⁵

a)

X¹∕ ⁵

b)

X ²⁄⁵

c)

X⁵⁄ ²

d)

X⁵

132.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

133.

Simplify (34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

134.

What was your answer for #2? Use the ^ button for exponents. Do not type spaces.

(a)

135.

What was your answer for #4. Use the ^ button for exponents. Do not type spaces.

(a)

136.

What was your answer for #6? Use the ^ button for exponents. Do not type spaces.

(a)

137.