Free Printable Exponent Rules

1.

a)

-30x¹¹

b)

-30x¹⁸

c)

-x¹¹

d)

-x¹⁸

2.

a)

y¹⁶⁰

b)

y¹

c)

1

d)

y⁴

3.

a)

-15x²yz⁴

b)

1

4.

a)

b)

16c³d³

c)

d)

5.

a)

b)

c)

3x⁴y

d)

6.

a)

b)

-7c⁹

c)

d)

7.

a)

b)

2x²z⁴

c)

3x²y⁵z⁴

d)

8.

a)

3ab⁸c³

b)

c)

d)

2ab⁸c¹¹

9.

a)

b)

-12x²y

c)

d)

-108xy²

10.

a)

b)

c)

d)

11.

a)

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

b)

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

c)

$27x^8yz^4$

d)

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

12.

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)

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

13.

(5x²y²)³

a)

125x⁶y⁶

b)

15x⁶y⁶

c)

8x⁵y⁵

d)

15x⁵y⁵

14.

$\left(\frac{-8p^{10}}{7r^3}\right)^{^2}$

a)

-64p²⁰/ 49r⁶

b)

64p²⁰/ 49r⁶

c)

-8p²⁰/ 14r⁶

d)

-64p¹²/ 49r⁵

15.

True or False?

a)

True

b)

False

16.

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

a)

add

b)

subtract

c)

multiply

d)

divide

17.

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

a)

add

b)

subtract

c)

multiply

d)

divide

18.

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

a)

add

b)

subtract

c)

multiply

d)

divide

19.

How do you solve:
(2x⁵)(6x⁴)

a)

MULTIPLY coefficients
MULTIPLY exponents

b)

DIVIDE coefficients
SUBTRACT exponents

c)

Combine like terms

d)

MULTIPLY coefficients
ADD exponents

20.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

21.

Simplify: (-4)²

a)

-8

b)

16

c)

-16

d)

8

22.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

23.

Simplify completely: 4²4³

a)

1024

b)

4⁶

c)

16⁵

d)

4⁵

24.

Simplify: (-5p)²

a)

-25p²

b)

25p²

c)

-5p²

d)

5p²

25.

Simplify: (2x/3)⁴

a)

(8x)/12

b)

(16x⁴)/81

c)

(8x)/81

d)

(2x⁴)/81

26.

Simplify: x¹⁰⋅x⁴

a)

x⁴⁰

b)

x¹⁴

c)

x⁶

d)

2x¹⁴

27.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

28.

Simplify: (6m⁷)/(4m³)²

a)

(6m)/16

b)

(3/8)m

c)

3/(8m)

d)

(3m)/4

29.

Simplify: x⁸/x²

a)

x¹⁶

b)

x⁴

c)

x⁵

d)

x⁶

30.

Simplify: 7p⁰

a)

7

b)

1

c)

simplified

d)

7p

31.

Simplify to an equivalent expression BUT leave in exponent form.
4³⋅4⁵

a)

4⁸

b)

16⁸

c)

4¹⁵

d)

16¹⁵

32.

evaluate ∛64

a)

-4

b)

4

c)

21.333

d)

-21.3333

33.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

34.

Simplify the expression.

a)

1

b)

g¹⁰

c)

g²⁵

d)

g

35.

Evaluate using the quotient rule:

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

36.

Simplify using the product rule: x³y²x³=

a)

x⁶y²

b)

xy⁸

c)

x³y⁵

37.

4⁰

a)

0

b)

1

c)

4

d)

-4

38.

Using exponents, simplify the following expression:

(f^-6)(f¹⁰)

a)

f¹⁶

b)

f⁴

c)

1/f⁴

d)

1/f¹⁶

39.

Rewrite using positive exponents

a)

2⁴

b)

1/2⁴

c)

4²

d)

1/4²

40.

Using exponents, simplify the following expression

a)

x^-7

b)

1/x⁷

c)

x⁷

d)

x^-9

41.

Which two exponent rules do you need to use to simplify this expression?

a)

Product Rule and Quotient Rule

b)

Power Rule and Negative Exponent Rule

c)

Power Rule and Product Rule

d)

Zero Rule and Power Rule

42.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

43.

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

a)

add

b)

subtract

c)

multiply

d)

divide

44.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

45.

(k¹⁷)²

a)

k¹⁹

b)

k¹⁵

c)

2k¹⁷

d)

k³⁴

46.

Evaluate the expression using the quotient rule.

a)

3⁴

b)

1/3⁴

c)

3^-12

d)

3³²

47.

Which expression is equivalent to the given?

a)

b)

c)

d)

48.

Simplify the following:
(x²y)⁵

a)

x⁷y⁵

b)

x²y⁵

c)

x¹⁰y⁵

d)

x⁵y⁵

49.

Which expression is equivalent to the given?

a)

b)

c)

d)

50.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

51.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

52.

Simplify: x²⋅ x⁵

a)

x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x

b)

x⁷

c)

x¹⁰

d)

x ⋅ x

53.

Simplify: 3x³ ⋅ 3x

a)

3²x⁴

b)

3 ⋅ x ⋅ x ⋅ x ⋅3 ⋅ x

c)

9x⁴

d)

3x⁴

54.

Simplify the expression: r⁶⋅r²⋅r³=

a)

r⁶⁺²⁺³

b)

r¹¹

c)

11r

55.

Simplify (2m⁴) x (5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

56.

Which is equivalent to 7 x 7 x 7 x 7 x 7 x 7

a)

7⁵

b)

7⁶

c)

6⁷

d)

7⁷

57.

Simplify the expression:
5²⋅5¹=

a)

5³

b)

5³⁺¹

c)

5²

58.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

59.

Simplify the expression.
x³x⁶

a)

x⁹

b)

x³

c)

x¹⁸

d)

x³⁶

60.

Which is equivalent to 5 x 5 x 5 x 5

a)

5³

b)

5⁴

c)

4⁵

d)

5⁵

61.

Simplify: 10³ x 10⁵

a)

10¹⁵

b)

10⁸

c)

10²

d)

10⁶

62.

Simplify: (10⁴)⁵

a)

10²⁰

b)

10¹

c)

10⁹

d)

10⁶

63.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

64.

Simplify: (2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

65.

Simplify: $6^5\cdot6^2$

a)

$6^7$

b)

$6^3$

c)

$36^7$

d)

$6^{10}$

66.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

67.

(c⁵)(c³)(c³)

a)

c⁴⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

68.

Using exponents, simplify the following expression:

\frac{x^5}{x^3}

a)

x²

b)

x

c)

1

d)

x⁸

69.

Simplify the following
(no negative exponents):

$\frac{xy^7}{x^3y^4}$

a)

$x^4y^{11}$

b)

$x^3y^{28}$

c)

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

d)

$\frac{x^4}{y^{11}}$

70.

simplify 7^-2

a)

1/7²= 1/49

b)

-49

c)

-14

d)

1/14

71.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

72.

8⁰ = 0

a)

True

b)

False

73.

Simplify: 7p⁰

a)

7

b)

1

c)

simplified

d)

7p

74.

$\frac{7^3}{7^{10}}$

a)

$7^7$

b)

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

c)

$7^{13}$

d)

$\frac{1}{7^{13}}$

75.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

76.

True or False:

a)

True

b)

False

77.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

78.

Simplify the expression.

a)

1

b)

g¹⁰

c)

g²⁵

d)

g

79.

Evaluate the expression using the quotient rule.

a)

3⁴

b)

1/3⁴

c)

3^-12

d)

3³²

80.

True or False?

a)

True

b)

False

81.

Simplify: $\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$

a)

$16a^8b^9c^9$

b)

$8a^8b^9c^9$

c)

$8a^6b^5c^6$

d)

$16a^5b^5c^6$

82.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

83.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

84.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

85.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

86.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

87.

3³ ⋅ 3

a)

3⁴

b)

3³

c)

3⁰

d)

1 ⁄ 3⁴

88.

Simplify
m⁵⋅m²

a)

m⁷

b)

m³

c)

m¹⁰

d)

m²

89.

Simplify
(y³)⁵

a)

y¹⁵

b)

y⁸

c)

y⁻²

d)

y

90.

Simplify: x¹⁰⋅x⁴

a)

x⁴⁰

b)

x¹⁴

c)

x⁶

d)

2x¹⁴

91.

Simplify: $6^5\cdot6^2$

a)

$6^7$

b)

$6^3$

c)

$36^7$

d)

$6^{10}$

92.

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

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

93.

Simplify: $10x^8\cdot9x$

a)

$90x^8$

b)

$19x^9$

c)

$90x^9$

d)

$19x^9$

94.

Simplify: $\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$

a)

$16a^8b^9c^9$

b)

$8a^8b^9c^9$

c)

$8a^6b^5c^6$

d)

$16a^5b^5c^6$

95.

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

a)

$1^3$

b)

$0^3$

c)

$2^3$

d)

$2^{15}$

96.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

97.

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

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

98.

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

a)

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

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

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

99.

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

a)

$10m^5$

b)

$32m^5$

c)

$25m^5$

d)

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

100.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

101.

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

a)

$5x^4$

b)

$-5x^4$

c)

$5x^3$

d)

$-5x^3$

102.

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

a)

$5k^2$

b)

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

c)

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

d)

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

103.

Simplify: $\left(\frac{4}{2d^2}\right)^3$

a)

$\frac{2}{d^2}$

b)

$\frac{8}{d^6}$

c)

$\frac{8}{2d^2}$

d)

$\frac{64}{2d^2}$

104.

Simplify: $\frac{\left(4x^2y^3\right)^0}{8x^3}$

a)

$\frac{1}{8x^3}$

b)

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

c)

$\frac{4y^3}{8x}$

d)

$1$

105.

Simplify: $6^5\cdot6^2$

a)

$6^7$

b)

$6^3$

c)

$36^7$

d)

$6^{10}$

106.

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

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

107.

Simplify: $10x^8\cdot9x$

a)

$90x^8$

b)

$19x^9$

c)

$90x^9$

d)

$19x^9$

108.

Simplify: $\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$

a)

$16a^8b^9c^9$

b)

$8a^8b^9c^9$

c)

$8a^6b^5c^6$

d)

$16a^5b^5c^6$

109.

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

a)

$1^3$

b)

$0^3$

c)

$2^3$

d)

$2^{15}$

110.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

111.

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

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

112.

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

a)

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

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

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

113.

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

a)

$10m^5$

b)

$32m^5$

c)

$25m^5$

d)

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

114.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

115.

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

a)

$5x^4$

b)

$-5x^4$

c)

$5x^3$

d)

$-5x^3$

116.

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

a)

$5k^2$

b)

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

c)

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

d)

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

117.

Simplify: $\left(\frac{4}{2d^2}\right)^3$

a)

$\frac{2}{d^2}$

b)

$\frac{8}{d^6}$

c)

$\frac{8}{2d^2}$

d)

$\frac{64}{2d^2}$

118.

Simplify: $\frac{\left(4x^2y^3\right)^0}{8x^3}$

a)

$\frac{1}{8x^3}$

b)

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

c)

$\frac{4y^3}{8x}$

d)

$1$

119.

Simplify: (-4)²

a)

-8

b)

16

c)

-16

d)

8

120.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

121.

Simplify completely: 4²4³

a)

1024

b)

4⁶

c)

16⁵

d)

4⁵

122.

Simplify: (-5p)²

a)

-25p²

b)

25p²

c)

-5p²

d)

5p²

123.

Simplify: (2x/3)⁴

a)

(8x)/12

b)

(16x⁴)/81

c)

(8x)/81

d)

(2x⁴)/81

124.

Simplify: x¹⁰⋅x⁴

a)

x⁴⁰

b)

x¹⁴

c)

x⁶

d)

2x¹⁴

125.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

126.

Simplify: (6m⁷)/(4m³)²

a)

(6m)/16

b)

(3/8)m

c)

3/(8m)

d)

(3m)/4

127.

Simplify: x⁸/x²

a)

x¹⁶

b)

x⁴

c)

x⁵

d)

x⁶

128.

Simplify: 7p⁰

a)

7

b)

1

c)

simplified

d)

7p

129.

Simplify the following: $\frac{2v^5}{8v^3}$

a)

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

b)

$4v^2$

c)

$-6v^8$

d)

$6v^8$

130.

Simplify the expression

a)

x⁵

b)

1/x⁵

c)

x¹³

d)

1/x¹³

131.

$7b^3\ \cdot\ 3b^2$

a)

$10b^6$

b)

$21b^6$

c)

$10b^5$

d)

$21b^5$

132.

$\frac{3x^2}{7x^2}$

a)

$\frac{3x}{7x}$

b)

$\frac{3}{7}$

c)

$\frac{3^2}{7^2}$

d)

$0.4285$

133.

Select ALL solutions that are equivalent to the following expression

a)

1/j³

b)

j^-23

c)

1/j²³

d)

j^-3

134.

$3x^2\ \cdot\ 7x^2\ \cdot\ 3x$

a)

$63x^5$

b)

$13x^4$

c)

$24x^4$

d)

$36x^2$

135.

$4n^2\ \cdot\ n$

a)

$4n^3$

b)

$4n$

c)

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

d)

$\frac{4}{n}$

136.

Simplify the expression

a)

x²/2

b)

2/x¹⁴

c)

2x¹⁴

d)

2/x²

137.

Simplify so there are no negative exponents in the answer.

\frac{3x^3\cdot4x^4}{x^2}

a)

$12x^5$

b)

$12x^9$

c)

$7x^5$

d)

$7x^4$

138.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

139.

Simplify the following: $\left(2v\right)^2\cdot2v^2$

a)

$2v^4$

b)

$8v^3$

c)

$2^2v^4$

d)

$8v^4$

140.

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

a)

$4x^{16}$

b)

$16x^8$

c)

$256x^{16}$

d)

$4x^8$

141.

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

a)

$9x^3$

b)

$x^3$

c)

$27x^3$

d)

$6x^3$

142.

$7x^0\cdot\ 5x^{3\ }$

a)

$35x^3$

b)

$35x^4$

c)

$2x^3$

d)

$35x^2$

143.

Simplify the following
(no negative exponents):
$\frac{-48c^2d^4}{8cd}$

a)

$-40cd^3$

b)

$-40c^3d^5$

c)

$\frac{c^3d^5}{6}$

d)

$-6cd^3$

144.

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

a)

$x^3y^9$

b)

$64x^3y^9$

c)

$12x^4y^6$

d)

$64x^4y^6$

Exponent Rules

Total questions: 144

Worksheet time: 6hrs 27mins

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