Free Printable laws of exponents

1.

Simplify 5³⋅5⁴

a)

5⁷

b)

5⁻¹

c)

5¹²

d)

5

2.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

3.

Solve and Simplify (no exponent)

2^0

a)

$0$

b)

$1$

c)

$2$

d)

$\frac{1}{2}$

4.

3⁴x 3⁷

a)

9²⁸

b)

3²⁸

c)

3¹¹

d)

9¹¹

5.

Simplify:
(x³)(x²)

a)

x⁵

b)

x⁶

c)

x

d)

x^1.5

6.

How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?

a)

5⁷

b)

5⁶

c)

7⁵

d)

5

7.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

8.

Simplify: $x^3\cdot x^4$

a)

$x^{12}$

b)

$x^7$

c)

$x^1$

d)

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

9.

Solve using the product law of exponents

(5⁵)(5³)

a)

25⁸

b)

5¹⁵

c)

25¹⁵

d)

5⁸

10.

Solve using the product law of exponents.

(10¹²)(10⁴)

a)

10¹⁶

b)

10⁴⁸

c)

100¹⁶

d)

100⁴⁸

11.

Simplify.

(x⁴) (x)

a)

2x⁴

b)

x

c)

x⁵

d)

x⁴

12.

5²·5⁵=

a)

5⁷

b)

5³

c)

5^-7

d)

5^-3

13.

x³·x⁴=

a)

x⁷

b)

x¹

c)

x^-7

d)

x^-1

14.

n⁰ =

a)

1

b)

0

15.

Simplify:

(x³)(x²)

a)

x⁵

b)

x⁶

c)

x

16.

How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?

a)

5⁷

b)

5⁶

c)

7⁵

d)

5

17.

Simplify the expression using exponential notation:

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

a)

$a^{12}$

b)

$a^7$

c)

$a$

d)

$a^{15}$

18.

Simplify the expression using exponential notation:

$\left(y^8\right)^5$

a)

$y^{13}$

b)

$y^{40}$

c)

$y^3$

d)

$y^{85}$

19.

$\frac{x^8}{x^5}$

a)

$x^3$

b)

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

c)

$x^{13}$

d)

$x^{40}$

20.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

21.

Simplify:
(x³)(x²)

a)

x⁵

b)

x⁶

c)

x

d)

x^1.5

22.

Simplify (-5.7)⁰

a)

1

b)

0

c)

-1

d)

-5.7

23.

a)

x¹²

b)

x^-12

c)

x²

d)

x^-2

24.

a)

w

b)

w^-1= 1/w

c)

-w

d)

w¹⁷

25.

a)

a⁷

b)

a¹⁰

c)

a³

d)

a^-3

26.

a)

3

b)

0

c)

1

d)

1/3

27.

a)

8

b)

1/8

c)

8⁷

d)

all of the above

28.

According to exponent rules, when we multiply the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

29.

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

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

30.

Simplify:
b²⋅ b⁴

a)

b⁸

b)

b⁶

c)

b²

d)

2b⁶

31.

Simplify:
(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

32.

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

a)

add

b)

subtract

c)

multiply

d)

divide

33.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

34.

Multiply

a)

100

b)

10¹

c)

10^-2

d)

1/100

35.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

36.

Simplify the expression using exponential notation:

$a^2\cdot a^4$

a)

$a^6$

b)

$a^8$

c)

$a^2$

d)

$a^{24}$

37.

Simplify the expression using exponential notation:

$x^5\cdot x^5$

a)

$x^{25}$

b)

$x^2$

c)

$x^{10}$

d)

x

38.

Simplify the expression using exponential notation:

$y^9\cdot y^8$

a)

$y^{72}$

b)

$y^{ }$

c)

$y^{17}$

d)

$y^3$

39.

Simplify the expression using exponential notation:

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

a)

$a^{12}$

b)

$a^7$

c)

$a$

d)

$a^{15}$

40.

Simplify the expression using exponential notation:

$\left(y^8\right)^5$

a)

$y^{13}$

b)

$y^{40}$

c)

$y^3$

d)

$y^{85}$

41.

Simplify the expression using exponential notation:

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

a)

$y^6$

b)

$y^9$

c)

$y^{15}$

d)

$y^5$

42.

$\left(7x^3\right)^0$

a)

1

b)

7

c)

$21x^3$

d)

$x^{10}$

43.

$k^{-6}$

a)

$\frac{k}{6}$

b)

$\frac{6}{k}$

c)

$k^6$

d)

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

44.

$\frac{x^8}{x^5}$

a)

$x^3$

b)

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

c)

$x^{13}$

d)

$x^{40}$

45.

According to exponent rules, when we multiply the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

46.

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

a)

add

b)

subtract

c)

multiply

d)

divide

47.

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

a)

$x$

b)

$x^2$

c)

$x^3$

d)

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

48.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

49.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

50.

Simplify the expression:
(5⁸) ÷ (5²)

a)

5⁶

b)

5¹⁰

c)

5⁴

d)

5¹⁶

51.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

52.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

53.

Simplify the expression in exponential form:
134⁰

a)

0

b)

134

c)

1

54.

z⁰

a)

z

b)

0

c)

1

55.

$Evaluate\ the\ \exp ression.\ \ \ \ \ 7^9\ \div\ \left(7^2\right)^3$

a)

$7^8$

b)

$7^4$

c)

$49^3$

d)

$7^3$

56.

$Evaluate\ \ \ \ 3\left(5^0\right).$

a)

15

b)

4

c)

3

d)

27

57.

15⁹÷15^{3 =}

a)

15⁶

b)

15¹²

c)

1⁶

d)

1¹²

58.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

59.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

60.

18h¹⁰÷ 6h⁸

a)

3h¹⁸

b)

3h⁸⁰

c)

2h²

d)

3h²

61.

12h⁸÷ 3h⁴

a)

4h¹²

b)

9h⁴

c)

4h⁴

d)

9h¹²

62.

Evaluate the expression using the quotient rule.

a)

1²²

b)

1³⁰

c)

6²²

d)

6³⁰

63.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

64.

Division Law states: keep the base the same and do this to the exponents.

a)

multiply

b)

add

c)

subtract

d)

divide

65.

30y¹²/ 15y²

a)

2y²⁴

b)

2¹⁰

c)

2y¹⁰

d)

2y¹⁴

66.

32x⁶ / 4x²

a)

8x⁴

b)

8x⁸

c)

6x⁴

d)

6x⁸

67.

Simplify

a)

x²⁸y¹² / x²y

b)

x²⁸y¹² / x⁸y⁴

c)

x²⁰y⁸

68.

a)

A

b)

B

c)

C

d)

D

69.

Simplify:
(12x⁵y⁴/16x²y⁶)^{2
Note: / is divide--rewrite first part over the second part to view easier}

a)

9x⁹/16y⁴

b)

144x¹⁰y⁸/256x⁴y¹²

c)

3x^6/4y⁴

d)

9x⁶/16y⁴

70.

True or False:

a)

True

b)

False

71.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

72.

Simplify the expression.

a)

1

b)

g¹⁰

c)

g²⁵

d)

g

73.

Simplify the expression.

a)

1²²

b)

1³⁰

c)

6²²

d)

6³⁰

74.

Evaluate the expression using the quotient rule.

a)

3⁴

b)

1/3⁴

c)

3^-12

d)

3³²

75.

Evaluate using the quotient rule:

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

76.

Quotient Rule states: keep the base the same and do this to the exponents.

a)

multiply

b)

add

c)

subtract

d)

divide

77.

Without a calculator, evaluate:
1^3,412 =

a)

3,412

b)

3,411

c)

0

d)

1

78.

True or False?

a)

True

b)

False

79.

True or False?

a)

True

b)

False

80.

Simplify using the product rule: x³y²x³=

a)

x⁶y²

b)

xy⁸

c)

x³y⁵

81.

Simplify the expression.
x⁴ (x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

82.

Simplify the expression.
(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

83.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

84.

n²⋅n⁴

a)

n²

b)

n⁸

c)

n⁶

d)

n²²

85.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

86.

Simplify the expression:
5²⋅5¹=

a)

5³

b)

5³⁺¹

c)

5²

87.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

88.

Simplify the expression: r⁶⋅r²⋅r³=

a)

r⁶⁺²⁺³

b)

r¹¹

c)

11r

89.

When there is no exponent connected to the base it means the power is 0?
Ex: x= x⁰

a)

True

b)

False

90.

Write the exponent form of this expression: n⋅n⋅n⋅s⋅s⋅s⋅2⋅2=

a)

2²⋅n³⋅s³

b)

2²ns⁶

c)

4(3n)(3s)

91.

Write the exponent form of this expression: (5⋅5⋅5)⋅(5⋅5)=

a)

125⋅25

b)

5³⋅5²

c)

5⁵

92.

Write the exponent form of this expression: (x⋅x⋅x)⋅(x⋅x)

a)

3x⋅2x

b)

5x

c)

x⁵

93.

10⁴=

a)

1000

b)

10

c)

400

94.

What special word do you use for the exponent of 3?

a)

squared

b)

cubed

c)

triangled

d)

boxed

95.

What operation do you use with exponents?

a)

addition

b)

subtraction

c)

multiplication

d)

division

96.

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

a)

squared

b)

cubed

c)

triangled

d)

boxed

97.

What is the exponent form for the factors
5 x 5 x 5?

a)

3⁵

b)

5³

98.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

99.

Simplify the following expression:

(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

100.

Simplify the following expression:

(b³)⁸

a)

b¹¹

b)

8b³

c)

b²⁴

d)

24b

101.

Simplify the following expression:

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

102.

Simplify the following expression:

(3x⁴y⁵)²

a)

9x⁸y¹⁰

b)

6x⁸y¹⁰

c)

3x⁸y¹⁰

d)

x⁸y¹⁰

103.

Simplify the following expression:

(3y⁴)²

a)

9y⁸

b)

9y⁶

c)

6y⁸

d)

6y⁶

104.

(2ab)³

a)

2³a³b³

b)

2ab³

c)

6a³b³

d)

6ab

105.

(5²)³

a)

5⁶

b)

5⁵

c)

5⁷

d)

5⁸

106.

(r⁴)⁶

a)

10r

b)

r¹⁰

c)

24r

d)

r²⁴

107.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

108.

Write this expression using positive exponent:

x^-7

a)

$x^7$

b)

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

c)

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

d)

$-\frac{7}{x}$

109.

Simplify (evaluate):
$7^{-2}$

a)

$\frac{1}{7^2}=\frac{1}{14}$

b)

$7^{-2}=\frac{1}{14}$

c)

$7^{-2}=-49$

d)

$\frac{1}{7^2}=\frac{1}{49}$

110.

Rewrite using a positive exponent.

$w^{-13}$

a)

$-w^{13}$

b)

$\frac{1}{w^{13}}$

c)

$\frac{1}{w^{-13}}$

d)

$-13w$

111.

Write with positive exponents:

a)

a^-2

b)

a²

c)

1/a¹

112.

Rewrite using a positive exponent.

$2w^{-13}$

a)

$\frac{w^{13}}{2}$

b)

$\frac{2}{w^{13}}$

c)

$-\frac{2w}{13}$

d)

$\frac{2}{w^{-13}}$

113.

Simplify (34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

114.

$\frac{a^{-5}}{b^8}$

Simplify.

a)

$ab^{13}$

b)

$\frac{1}{a^5b^8}$

c)

$a^8b^5$

d)

$\frac{b^8}{a^5}$

115.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

116.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

117.

Simplify

a)

$4x$

b)

$x^4$

c)

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

d)

$\frac{1}{x^{14}}$

118.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

119.

Simplify

a)

$7ab^2$

b)

$\frac{a^5}{7b^3}$

c)

$7ab^8$

d)

$\frac{7b^3}{a^5}$

120.

$10x^{-3}y^{-2}$

Rewrite using positive exponents.

a)

$\frac{10}{x^3y^2}$

b)

$10xy^6$

c)

$\frac{x^3y^2}{10}$

d)

$\frac{x^3}{10y^2}$

121.

a)

x²y⁴

b)

x³y⁴

c)

x²/y⁴

d)

x²/y⁵

122.

$\frac{xy^{-8}}{4}$

Simplify the expression.

a)

$\frac{y}{4x^8}$

b)

$\frac{x}{4y^8}$

c)

$\frac{4x}{y^8}$

d)

$\frac{xy^8}{-4}$

123.

$\frac{a^5}{b^{-6}}$

Simplify the expression.

a)

$a^5b^6$

b)

$ab^{11}$

c)

$\frac{1}{a^5b^6}$

d)

none of these

124.

Simplify the expression so that it contains only positive exponents.

a)

b)

c)

d)

125.

Simplify the expression so that it contains only positive exponents.

a)

b)

c)

d)

126.

Simplify the expression so that it contains only positive exponents.

a)

b)

c)

d)

127.

Simplify each expression so that it contains only positive exponents.

a)

b)

c)

d)

128.

a)

$b$

b)

$\frac{1}{b}$

c)

$b^7$

d)

$b^{12}$

129.

$\frac{x^8y^6}{x^9y^2}$

a)

$xy^3$

b)

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

c)

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

d)

$\frac{xy^{14}}{xy^{11}}$

130.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

131.

Simplify
(-7y²)(5y⁴)

a)

-35y⁶

b)

-2y⁶

c)

-35y⁸

d)

-2y⁸

132.

Simplify:

a)

a²

b)

a³

c)

a⁴

d)

a⁵

133.

Simplify:

a)

a

b)

a²

c)

a³

d)

a⁴

134.

Simplify:

a)

a

b)

a²

c)

a³

d)

a⁴

135.

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

a)

$x^{\frac{4}{3}}y^{\frac{5}{2}}$

b)

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

c)

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

d)

$x^{\frac{2}{3}}y^{\frac{4}{3}}$

136.

Simplify . Your answer should contain only positive exponents. $\frac{2x^{\frac{1}{2}}y^{\frac{1}{3}}}{x^{\frac{4}{3}}y^{-\frac{7}{4}}}$

a)

$\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

b)

$\frac{x^{\frac{5}{6}}}{y^{\frac{25}{12}}}$

c)

$\frac{2y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

d)

$\frac{y^{\frac{17}{12}}}{x^{\frac{5}{6}}}$

137.

a)

-30x¹¹

b)

-30x¹⁸

c)

-x¹¹

d)

-x¹⁸

138.

a)

-15x²yz⁴

b)

1

139.

a)

-30a²⁰c

b)

7a¹³b⁵c

c)

7a²⁰c

d)

-30a¹³b⁵c

140.

a)

$\frac{1}{16}$

b)

$\frac{1}{8}$

c)

-16

d)

-8

141.

a)

$\frac{1}{27}$

b)

$\frac{1}{-9}$

c)

27

d)

9

142.

a)

b)

16c³d³

c)

d)

143.

a)

b)

c)

3x⁴y

d)

144.

a)

b)

-7c⁹

c)

d)

145.

a)

x⁷

b)

x¹¹

c)

d)

146.

a)

b)

c)

1

d)

0

147.

a)

b)

z^-11

c)

z

d)

z¹¹

148.

a)

b)

2x²z⁴

c)

3x²y⁵z⁴

d)

149.

a)

3ab⁸c³

b)

c)

d)

2ab⁸c¹¹

150.

a)

b)

-12x²y

c)

d)

-108xy²

151.

a)

b)

c)

d)

152.

a)

$25x^{22}$

b)

$10x^{22}$

c)

$25x^{13}$

d)

$-25x^{22}$

153.

a)

$\frac{27x^{15}z^3}{y^6}$

b)

$\frac{9x^{15}z^3}{y^6}$

c)

$27x^8yz^4$

d)

$\frac{27x^8z^4}{y}$

154.

a)

$\frac{16x^{16}z^{32}}{y^{28}}$

b)

$\frac{-16x^{16}z^{32}}{y^{28}}$

c)

$\frac{x^{16}z^{32}}{16y^{28}}$

d)

$-8x^{-8}y^3z^{-12}$

155.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

156.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

157.

a)

b)

c)

d)

158.

a)

b)

c)

d)

159.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

160.

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

a)

add

b)

subtract

c)

multiply

d)

divide

161.

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

a)

True

b)

False

162.

Simplify $\left(\frac{x^4}{y^{-2}}\right)^3$

a)

$x^{12}y^6$

b)

$\frac{x^{12}}{y^{-6}}$

c)

$x^7y$

d)

$\frac{y^6}{x^{12}}$

163.

If the area of a rectangle is $42x^8y^6$ and length is $7x^2y^3$ what is the width?

a)

$6x^4y^2$

b)

$49x^{10}y^9$

c)

$6x^6y^3$

d)

$35x^6y^3$

164.

a)

10t²

b)

10/t²

c)

18t²

d)

2t

165.

Simplify:

a)

x⁶y⁴

b)

x²y⁴

c)

x⁸y⁴

d)

x⁸y

166.

If (2^x)⁵=2¹⁵, what does x equal?

a)

x = 3

b)

x = 5

c)

x = 10

167.

$\left(4x^2\right)^3$ is the same as...

a)

$\left(4\cdot3\cdot x\cdot x\right)\left(4\cdot3\cdot x\cdot x\right)$

b)

$\left(4\cdot x\cdot x\cdot3\right)$

c)

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

laws of exponents

Total questions: 167

Worksheet time: 14hrs 34mins

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