Free Printable Exponent Rules

1.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

2.

Simplify the expression.
x⁴ (x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

3.

Simplify the following expression:

(xyz)⁰ =

a)

0

b)

1

c)

xyz

d)

-1

4.

Evaluate using the quotient rule:

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

5.

Simplify: $\frac{9h^6}{3h^3}$

a)

$3h^9$

b)

$3h^{3\ }$

c)

$3h^{18}$

d)

$h^{3\ }$

6.

Simplify

a)

\frac{x^{28}y^{12}}{x^2y}

b)

$\frac{x^{28}y^{12}}{x^8y^4}$

c)

$x^{20}y^8$

7.

Simplify using your exponent rule(s) (2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

8.

Using exponents, simplify the following expression:

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

a)

x²

b)

x

c)

1

d)

x⁸

9.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

10.

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

11.

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

12.

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

13.

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

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

14.

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)

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

15.

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)

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

16.

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

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

17.

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

a)

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

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

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

18.

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

a)

$10m^5$

b)

$32m^5$

c)

$25m^5$

d)

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

19.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

20.

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

a)

$5x^4$

b)

$-5x^4$

c)

$5x^3$

d)

$-5x^3$

21.

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

a)

$5k^2$

b)

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

c)

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

d)

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

22.

Simplify: $\left(3k^5\right)\left(-2k^3\right)$

a)

$6k^8$

b)

$-6k^{15}$

c)

$6k^{15}$

d)

$-6k^8$

23.

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

a)

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

b)

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

c)

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

d)

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

24.

Simplify: $\frac{-15x^9}{10x^{17}}$

a)

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

b)

$\frac{-3x^8}{2}$

c)

$\frac{-3x^{-8}}{2}$

d)

$\frac{-3}{2x^8}$

25.

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)

$1$

26.

Simplify: $\frac{50r^6n^{-7}}{2n^2r^4}$

a)

$25r^4n^5$

b)

$\frac{25r^4}{n^5}$

c)

$\frac{25r^2}{n^9}$

d)

$25r^2n^{-9}$

27.

Using exponents, simplify the following expression:

(f^-6)(f¹⁰)

a)

f¹⁶

b)

f⁴

c)

1/f⁴

d)

1/f¹⁶

28.

Simplify the following expression:

-9⁰

a)

-9

b)

0

c)

-1

d)

1

29.

Using exponents, simplify the following expression

a)

x^-7

b)

1/x⁷

c)

x⁷

d)

x^-9

30.

Simplify the expression

a)

x⁵

b)

1/x⁵

c)

x¹³

d)

1/x¹³

31.

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

32.

Select ALL solutions that are equivalent to the following expression

a)

1/j³

b)

j^-23

c)

1/j²³

d)

j^-3

33.

A coefficient is __________.

a)

the variable

b)

a constant

c)

an exponent

d)

the number that comes before the variable

34.

a)

-15x²yz⁴

b)

1

35.

a)

b)

16c³d³

c)

d)

36.

a)

b)

c)

3x⁴y

d)

37.

a)

b)

-7c⁹

c)

d)

38.

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)

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

39.

t⁹ x t⁸

a)

t¹

b)

t⁷²

c)

t¹⁷

d)

t

40.

(r⁴)⁶

a)

10r

b)

r¹⁰

c)

24r

d)

r²⁴

41.

Simplify: (3x²)³

a)

27x⁶

b)

9x⁶

c)

3x⁶

d)

9x⁵

42.

Simplify:
(5ab²)²

a)

25a²b⁴

b)

10a²b⁴

c)

5a²b⁴

d)

25ab²

43.

5³⋅5⁴

a)

5⁷

b)

5⁻¹

c)

5¹²

d)

5

44.

(c⁵)(c³)(c³)

a)

c⁴⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

45.

(x⁴)²

a)

x⁸

b)

x⁶

c)

x²

d)

8

46.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

47.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

48.

Simplify the expression:
(5⁸) ÷ (5²)

a)

5⁶

b)

5¹⁰

c)

5⁴

d)

5¹⁶

49.

Simplify the expression in exponential form:
134⁰

a)

0

b)

134

c)

1

50.

Simplify the expression:
(a⁵)(a⁴)

a)

a²⁰

b)

a⁹

c)

a¹

51.

Simplify (2x⁴y⁷)³

a)

6x⁷y¹⁰

b)

6xy³²

c)

8x¹²y²¹

d)

8x⁷y¹⁰

52.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

53.

Simplify m¹²/ m³

a)

m^12-3 = m⁹

b)

m^12/3= m⁴

c)

m^-9

d)

-m⁹

54.

simplify 7^-2

a)

1/7²= 1/49

b)

-49

c)

-14

d)

1/14

55.

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

a)

add

b)

subtract

c)

multiply

d)

divide

56.

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

a)

add

b)

subtract

c)

multiply

d)

divide

57.

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

a)

add

b)

subtract

c)

multiply

d)

divide

58.

5^-3 = 1

a)

True

b)

False

59.

8⁰ = 0

a)

True

b)

False

60.

7⁸/7⁴ = 7²

a)

True

b)

False

61.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

62.

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

63.

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

64.

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

65.

Simplify using your exponent rule(s) (-2)³⋅(-2)⁶

a)

(-2)⁹

b)

(-2)¹⁸

c)

(-2)⁻³

d)

(-2)

66.

Simplify using your exponent rule(s) x⁵⁄x³

a)

x²

b)

x

c)

1

d)

x⁸

67.

Simplify using your exponent rule(s) x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

68.

Simplify using your exponent rule(s) -14x⁷/7x

a)

-2x⁶

b)

-2x

c)

-2x⁵

d)

-2x⁸

69.

Simplify using your exponent rule(s) (5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

70.

Find the missing exponent:
5y² . (2y³)^x= 80y¹⁴

a)

x = 9

b)

x = 4

c)

x = 3

d)

x = 2

71.

Find the area of the triangle given (BH/2):

B = 3b²

H = 12p⁷b¹⁹

a)

18b²¹p⁷

b)

18b⁷p²¹

c)

36b²¹p⁷

d)

36b³⁸p⁷

72.

Rewrite using positive exponents

a)

2⁴

b)

1/2⁴

c)

4²

d)

1/4²

73.

Simplify using your exponent rule(s) (2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

74.

True or False?

a)

True

b)

False

75.

Can you leave a negative exponent in your answer?

a)

YES

b)

NO

76.

a)

-30x¹¹

b)

-30x¹⁸

c)

-x¹¹

d)

-x¹⁸

77.

a)

y¹⁶⁰

b)

y¹

c)

1

d)

y⁴

78.

a)

-15x²yz⁴

b)

1

79.

a)

b)

16c³d³

c)

d)

80.

a)

b)

c)

3x⁴y

d)

81.

a)

b)

-7c⁹

c)

d)

82.

a)

b)

2x²z⁴

c)

3x²y⁵z⁴

d)

83.

a)

3ab⁸c³

b)

c)

d)

2ab⁸c¹¹

84.

a)

b)

-12x²y

c)

d)

-108xy²

85.

a)

b)

c)

d)

86.

a)

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

b)

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

c)

$27x^8yz^4$

d)

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

87.

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)

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

88.

(5x²y²)³

a)

125x⁶y⁶

b)

15x⁶y⁶

c)

8x⁵y⁵

d)

15x⁵y⁵

89.

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

a)

-64p²⁰/ 49r⁶

b)

64p²⁰/ 49r⁶

c)

-8p²⁰/ 14r⁶

d)

-64p¹²/ 49r⁵

90.

True or False?

a)

True

b)

False

91.

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

a)

add

b)

subtract

c)

multiply

d)

divide

92.

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

a)

add

b)

subtract

c)

multiply

d)

divide

93.

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

a)

add

b)

subtract

c)

multiply

d)

divide

94.

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

95.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

96.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

97.

Simplify: x¹⁰⋅x⁴

a)

x⁴⁰

b)

x¹⁴

c)

x⁶

d)

2x¹⁴

98.

Simplify: x⁸/x²

a)

x¹⁶

b)

x⁴

c)

x⁵

d)

x⁶

99.

Simplify: 7p⁰

a)

7

b)

1

c)

simplified

d)

7p

100.

(c⁵)(c³)(c³)

a)

c⁴⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

101.

Simplify the expression in exponential form:
134⁰

a)

0

b)

134

c)

1

102.

Simplify (2x⁴y⁷)³

a)

6x⁷y¹⁰

b)

6xy³²

c)

8x¹²y²¹

d)

8x⁷y¹⁰

103.

simplify 7^-2

a)

1/7²= 1/49

b)

-49

c)

-14

d)

1/14

104.

5^-3 = 1

a)

True

b)

False

105.

8⁰ = 0

a)

True

b)

False

106.

7⁸/7⁴ = 7²

a)

True

b)

False

107.

Using exponents, simplify the following expression:

5⁵* 5^-3

a)

5^-15

b)

5⁸

c)

5^-8

d)

5²

108.

Simplify the following expression:

(xyz)⁰ =

a)

0

b)

1

c)

xyz

d)

-1

109.

Rewrite using positive exponents

a)

2⁴

b)

1/2⁴

c)

4²

d)

1/4²

110.

Simplify the expression

a)

x⁵

b)

1/x⁵

c)

x¹³

d)

1/x¹³

111.

Which is equivalent to 5 x 5 x 5 x 5

a)

5³

b)

5⁴

c)

4⁵

d)

5⁵

112.

In 2³what is the exponent?

a)

2

b)

3

c)

2³

113.

$4n^2\ \cdot\ n$

a)

$4n^3$

b)

$4n$

c)

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

d)

$\frac{4}{n}$

114.

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

a)

$9x^3$

b)

$x^3$

c)

$27x^3$

d)

$6x^3$

115.

$8v^{-3}$

a)

$8\ \cdot\ -v\ \cdot\ -v\ \cdot\ -v\$

b)

$\frac{v^3}{-8}$

c)

$-8v^3$

d)

$\frac{8}{v^3}$

116.

Simplify:

a)

4x⁸

b)

4x²

c)

4x¹⁴

d)

2.5x²

117.

a)

8x⁴

b)

8x⁸

c)

6x⁴

d)

6x⁸

118.

Application:
What is the area of the rectangle with the given sides?

a)

7x³y⁸z⁴

b)

10x²y¹⁶z³

c)

10x³y⁸z⁴

d)

none of the above

119.

a)

A

b)

B

c)

C

d)

D

120.

(a^m)ⁿ = a^mn, This rule says that to raise a power to a power you need to multiply the exponents.

a)

Product Rule

b)

Quotient rule

c)

Power of a Power Rule

d)

Negative Exponent Rule

e)

Zero exponent Rule

121.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

122.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

123.

Simplify
(-7y²)(5y⁴)

a)

-35y⁶

b)

-2y⁶

c)

-35y⁸

d)

-2y⁸

124.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

125.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

126.

Make this negative exponent positive.
9^-3

a)

9³

b)

1/9^-3

c)

1/9³

d)

729

127.

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

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

128.

Simplify the expression in exponential form:
(5⁴)^{3
Hint: Expand it out}

a)

5¹

b)

5⁷

c)

5¹²

129.

Simplify the expression in exponential form:
134⁰

a)

0

b)

134

c)

1

130.

Simplify the expression:
(a⁵)(a⁴)

a)

a²⁰

b)

a⁹

c)

a¹

131.

What's the base?
y⁵

a)

5

b)

y

132.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

133.

Simplify (-1/2)⁰

a)

1

b)

0

c)

-1

d)

-2

Exponent Rules

Total questions: 133

Worksheet time: 11hrs 9mins

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