Free Printable LAWS OF EXPONENTS (A)

1.

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

a)

5⁷

b)

5⁶

c)

7⁵

d)

5

2.

Rewrite the expression so that the exponent is positive.
9^-3

a)

9³

b)

1/9^-3

c)

1/9³

d)

729

3.

Zero Exponent Law states that _____ becomes equal to 1.

a)

the exponent

b)

the base

c)

nothing

d)

the whole term

4.

According to exponent rules, when we multiply terms with the same base,

we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

5.

According to exponent rules, when we divide terms with the same base,

we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

6.

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

a)

multiply

b)

add

c)

subtract

d)

divide

7.

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

a)

multiply

b)

add

c)

subtract

d)

divide

8.

$\left(3x^4\right)^5$

a)

$15x^9$

b)

$243x^{20}$

c)

$15x^{20}$

d)

$243x^9$

9.

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

a)

1

b)

7

c)

$21x^3$

d)

$x^{10}$

10.

$7x^0$

a)

1

b)

7

c)

$x^7$

d)

$x^{-7}$

11.

$\frac{1}{a^{-5}}$

a)

$a^{-5}$

b)

$\frac{a}{5}$

c)

$a^5$

d)

$\frac{5}{a}$

12.

$k^{-6}$

a)

$\frac{k}{6}$

b)

$\frac{6}{k}$

c)

$k^6$

d)

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

13.

$\left(-7x^2\right)\left(4x^4\right)$

a)

$-28x^8$

b)

$-28x^6$

c)

$-3x^8$

d)

$-3x^6$

14.

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

a)

$x^3$

b)

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

c)

$x^{13}$

d)

$x^{40}$

15.

$\left(-2x^3y^2\right)\left(5xy^4\right)$

a)

$3x^3y^8$

b)

$3x^4y^6$

c)

$-10x^3y^8$

d)

$-10x^4y^6$

16.

$4z^4\cdot6z^{-6}$

a)

$\frac{24}{z^2}$

b)

$24z^{-24}$

c)

$\frac{10}{z^2}$

d)

$10z^{-24}$

17.

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

a)

$x^2y^2$

b)

$3xy$

c)

$3x^2y^2$

d)

$\frac{xy}{3xy}$

18.

$\left(y^9\right)^{-2}$

a)

y¹⁸

b)

y¹¹

c)

$\frac{1}{y^{18}}$

d)

$\frac{y^9}{2}$

19.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

20.

Simplify:
(x³)⁴

a)

x⁷

b)

x¹²

c)

x^-1

d)

x^3/4

21.

Simplify the following:
(x²y)⁵

a)

x⁷y⁵

b)

x²y⁵

c)

x¹⁰y⁵

d)

x⁵y⁵

22.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

23.

Simplify:
b²⋅ b⁴

a)

b⁸

b)

b⁶

c)

b²

d)

2b⁶

24.

Simplify:
(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

25.

(x³y)⁶

a)

2x¹⁸y⁶

b)

x¹⁸y⁶

c)

x³y⁶

d)

x³y⁶

26.

Simplify (-1/2)⁰

a)

1

b)

0

c)

-1

d)

-2

27.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

28.

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

a)

add

b)

subtract

c)

multiply

d)

divide

29.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

30.

Multiply

a)

100

b)

10¹

c)

10^-2

d)

1/100

31.

a)

6^-2

b)

1/6²

c)

1/36

d)

All of the above

32.

a)

4⁹

b)

4⁴⁴

c)

4²¹

d)

4¹⁵

33.

a)

0

b)

3

c)

1

d)

-1

34.

a)

w

b)

w^-1= 1/w

c)

-w

d)

w¹⁷

35.

a)

a⁷

b)

a¹⁰

c)

a³

d)

a^-3

36.

a)

25⁶⁰

b)

25¹⁷

c)

5⁶⁰

d)

5¹⁷

37.

a)

1

b)

6⁰

c)

36/36

d)

all of the above

38.

Solve and Simplify (no exponent)

3^{-4}\times3^3

a)

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

b)

$3^{-1}$

c)

$\frac{1}{3}$

d)

$\frac{1}{2187}$

39.

Solve and Simplify (no exponent)

2^0

a)

$0$

b)

$1$

c)

$2$

d)

$\frac{1}{2}$

40.

Solve and Simplify (no exponent)

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

a)

$\frac{1}{4}$

b)

$16$

c)

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

d)

$\frac{1}{16}$

41.

Solve and Simplify (no exponent)

\left(2\cdot3\right)^2

a)

$36$

b)

$12$

c)

$24$

d)

$\frac{1}{36}$

42.

Solve and Simplify (no exponent)

3^{-3}

a)

$27$

b)

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

c)

$3^3$

d)

$\frac{1}{27}$

43.

Solve and Simplify (no exponent)

2^1

a)

$2$

b)

$\frac{1}{2}$

c)

$4$

d)

$\frac{1}{4}$

44.

Solve and Simplify (no exponent)

\left(2^2\right)^3

a)

$2^6$

b)

$64$

c)

$2^5$

d)

$32$

45.

Solve and Simplify (no exponent)

2^4\cdot2^{-2}

a)

$2^6$

b)

$2^2$

c)

$64$

d)

$4$

46.

Solve and Simplify (no exponent)

2^0

a)

$0$

b)

$1$

c)

$2$

d)

$\frac{1}{2}$

47.

Solve and Simplify (no exponent)

3^3\cdot3^4

a)

$3^7$

b)

$2187$

c)

$3$

d)

$4$

48.

(2ab)³

a)

2³a³b³

b)

2ab³

c)

6a³b³

d)

6ab

49.

y⁻¹¹⋅y⁵

a)

1⁄y⁶

b)

y⁶

c)

-y⁶

d)

-1⁄y⁶

50.

Simplify:
(3t²)³

a)

9t⁶

b)

9t⁵

c)

27t⁶

d)

27t⁵

51.

a)

-6c⁵

b)

-6c

c)

6c

d)

-6c⁶

52.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x¹⁰

d)

3x⁷

53.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

54.

x^-3

a)

1/x³

b)

1/x^-3

c)

3x

d)

1/3x

55.

(4x)³

a)

7x³

b)

64x³

c)

12x³

d)

16x³

56.

(2³)(2²)

a)

64

b)

8

c)

32

d)

4

57.

(x²)³

a)

x⁵

b)

x⁶

c)

x¹

d)

x^-1

58.

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

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

59.

Simplify (-1/2)⁰

a)

1

b)

0

c)

-1

d)

-2

60.

(x³y)⁶

a)

2x¹⁸y⁶

b)

x¹⁸y⁶

c)

x³y⁶

d)

x³y⁶

61.

3⁴is equal to which of the following?

a)

3 x 4

b)

4 x 4 x 4

c)

3 x 3 x 3 x 3

d)

(3)(4)

62.

Simplify:
x ∙ x ∙ x ∙ x ∙ x ∙ x

a)

x⁶

b)

6x

c)

x³

d)

6x⁶

63.

Simplify the expression using exponential notation:

$a^2\cdot a^4$

a)

$a^6$

b)

$a^8$

c)

$a^2$

d)

$a^{24}$

64.

Simplify the expression using exponential notation:

$x^5\cdot x^5$

a)

$x^{25}$

b)

$x^2$

c)

$x^{10}$

d)

x

65.

Simplify the expression using exponential notation:

$2^4x^2x^3x^4$

a)

$2^4x^9$

b)

$2x^9$

c)

$2^9x^4$

d)

$2^4x^{24}$

66.

Simplify the expression using exponential notation:

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

a)

$a^{12}$

b)

$a^7$

c)

$a$

d)

$a^{15}$

67.

Simplify the expression using exponential notation:

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

a)

$y^{13}$

b)

$y^{40}$

c)

$y^3$

d)

$y^{85}$

68.

Simplify the expression using exponential notation:

$\left(5x^7y\right)^4\cdot\left(5x^3y^8\right)^2$

*You NEED to combine like terms*

a)

$5^6x^{34}y^{20}$

b)

$5^4x^{28}y^{24}5^2x^6y^{16}$

c)

$5^2x^{22}y^{12}$

d)

$5^6x^{16}y^{20}$

69.

Simplify the expression using exponential notation:

$\left(7^2m^9n^3\right)^7$

a)

$7^{14}m^{63}n^{21}$

b)

$7^9m^{16}n^{10}$

c)

$7^5m^2n^4$

d)

$7^2m^9n^3$

70.

Simplify the expression using exponential notation:

$\frac{m^5n^6}{m}$

a)

$m^6n^6$

b)

$m^4n^6$

c)

$m^3n$

d)

$mn$

71.

Simplify each expression using exponential notation:

$\frac{4^2y^8}{4^3y^2}$

a)

$4y^6$

b)

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

c)

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

d)

$y^64$

72.

Simplify each expression using exponential notation:

$\frac{a^5b^{12}}{a^4b^9}$

a)

$b^3a$

b)

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

c)

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

d)

$ab^3$

73.

Simplify each expression using exponential notation:

$\frac{6^3k^{15}}{6^7k^{19}}$

a)

$k^46^4$

b)

$\frac{k^4}{6^4}$

c)

$6^4k^4$

d)

$\frac{6^4}{k^4}$

74.

Simplify each expression using exponential notation:

$\frac{a^7b^6c^8}{b^{10}c^9}$

a)

$\frac{a^7c}{b^4}$

b)

$\frac{a^7}{b^4c}$

c)

$a^7b^4c$

d)

$\frac{b^4c}{a^7}$

75.

Simplify each expression using exponential notation:

$\left(\frac{xy^2}{y}\right)^6$

*You might have an extra step*

a)

$x^6y^6$

b)

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

c)

$y^6x^6$

d)

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

76.

Simplify each expression using exponential notation:

$\left(\frac{8k^2}{k^3}\right)^2$

a)

$8^2k^4k^6$

b)

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

c)

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

d)

$k^28^2$

77.

Simplify each expression using exponential notation:

$\left(\frac{10a^3b^2}{a^2b^3}\right)^3$

Complete the extra step

a)

$\frac{10^3a^3}{b^3}$

b)

$\frac{10^3a^3b^6}{a^6b^9}$

c)

$10^3a^3b^3$

d)

$\frac{b^3}{10^3a^3}$

78.

Simplify each expression using exponential notation:

$\left(\frac{3x^7}{5}\right)^4$

a)

$\frac{x^{28}3^4}{5^4}$

b)

$\frac{5^4}{3^4x^{28}}$

c)

$3^4x^{28}5^{14}$

d)

$\frac{3^4x^{28}}{5^4}$

79.

Simplify each expression using exponential notation:

$\left(\frac{12^2}{3m^8n^6}\right)^2$

a)

$12^43^2m^{16}n^{12}$

b)

$\frac{12^4}{3^2m^{16}n^{12}}$

c)

$\frac{3^2m^{16}n^{12}}{12^4}$

d)

$3^212^4m^{16}n^{12}$

80.

5⁶written in standard form is

a)

6 x 6 x 6 x 6 x 6

b)

5 x 6

c)

5 x 5 x 5 x 5 x 5 x 5

d)

5 x 5

81.

b x b x b x b written in exponential form is

a)

b^x

b)

b⁴

c)

b⁵

d)

b^b

82.

Simplify:

12² x 2³ x 12⁵ x 2²

a)

12⁷ x 2⁵

b)

12¹⁰x 2⁶

c)

12⁵x 2¹⁰

d)

567⁶⁰

83.

5⁰=

(a)

84.

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

a)

add

b)

subtract

c)

multiply

d)

divide

85.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

86.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

87.

Which expression is equivalent to the given?

a)

b)

c)

d)

88.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

89.

Which expression is equivalent to the given?

a)

b)

c)

d)

90.

Simplify and evaluate $4a^0+\left(6b\right)^0$

a)

5

b)

0

c)

1

d)

$4+6b$

91.

Simplify $3\left[\left(x^2\right)^3\right]^0$

a)

0

b)

1

c)

3

d)

$3x^6$

92.

Tell whether the following question is TRUE or FALSE. $\left(4x^3y^4\right)^2=16x^6y^8$

a)

TRUE

b)

FALSE

93.

When simplified $\left(-3x^2\right)^2\left(4x^3\right)$ equals to

a)

$-36x^{12}$

b)

$36x^7$

c)

$-36x^7$

d)

$36x^{12}$

94.

Simplify the expression: $\frac{\left(-6x^2\right)^3}{\left(3x^{-4}\right)^2}$

a)

$-24x^{14}$

b)

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

c)

$\frac{x^{10}}{8y^4}$

d)

$\frac{1}{16x^8y^4}$

95.

Which expression is equivalent to $\frac{18c^8d^9}{9c^3d^6}$ ?

a)

$9c^{11}d^{15}$

b)

$2c^5d^3$

c)

$9c^5d^3$

d)

$2c^{11}d^{15}$

96.

Which is equivalent to expression below? $\frac{xy\left(24x^2y^3w\right)}{36y^5w^2}$

a)

$\frac{12x^3y}{w}$

b)

$\frac{x^2yw}{12}$

c)

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

d)

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

97.

Which is a simplified form of the following expression using only positive exponents? $\frac{10x^{-3}}{2y^5}$

a)

$\frac{1}{5x^3y^5}$

b)

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

c)

$\frac{1}{x^3y^5}$

d)

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

98.

Which is a simplified form of the following expression using only positive exponents? $\left(3a^{-2}b^3\right)\left(a^{-5}\right)$

a)

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

b)

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

c)

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

d)

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

99.

Which is a simplified form of the following expression using only positive exponents? $-2x^2y^{-5}z^{-7}$

a)

$\frac{1}{2x^2y^5z^7}$

b)

$\frac{y^5z^7}{-2x^2}$

c)

$\frac{-2x^2}{y^5z^7}$

d)

$\frac{-2}{x^2y^5z^7}$

100.

Which represent this expression in SIMPLEST FORM?

$\frac{20\left(x^{-2}\right)^3}{5\left(x^{-4}\right)^{-3}}$

a)

$15x^{18}$

b)

$4x^6$

c)

$\frac{15}{x^6}$

d)

$\frac{4}{x^{18}}$

101.

Simplify: $xy\cdot\left(2x^2y^3\right)$

a)

$2x^3y^4$

b)

$2x^3y^5$

c)

$x^3y^5$

d)

$2x^3$

102.

If $x\ne0$ and $y\ne0$ , which is equivalent to the following expression? $\frac{-24x^5y^4}{3xy^2}$

a)

$8x^4y^2$

b)

$-8x^6y^6$

c)

$-8x^5y^2$

d)

$-8x^4y^2$

103.

Which is the simplified form of the following expression using only positive exponents? $\frac{12x^{-5}}{4x^3y^2}$

a)

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

b)

$\frac{1}{3x^8y^2}$

c)

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

d)

$3x^8y^2$

104.

Which among the choices is equivalent to $\left(2x^5y^2\right)\left(4xy^3\right)+\left(x^4y^4\right)\left(3x^2y\right)$

a)

$8x^6y^5$

b)

$3x^6y^5$

c)

$11x^6y^5$

d)

$5x^6y^5$

105.

Simplify the expression: $2m^{10}n^2\left(-7m^9n^5\right)^2-\left(-m^7n^3\right)^4=$

a)

$98m^{28}n^{12}$

b)

$97m^{28}n^{12}$

c)

$96m^{28}n^{12}$

d)

$-15m^{28}n^{12}$

106.

Simplify.

$s^{-5}\cdot s^{-2}$

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

107.

Simplify.
2x^-5y⁷⋅3x^-4y^-2

a)

6x⁹y⁹

b)

6y⁵/x⁹

c)

6/x⁹y⁵

d)

6/x⁹y⁹

108.

Simplify the following expression: $xy^{-7}$

a)

xy⁷

b)

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

c)

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

d)

x⁷y

109.

Simplify and evaluate $4a^0+\left(6b\right)^0$

a)

5

b)

0

c)

1

d)

$4+6b$

110.

Simplify $3\left[\left(x^2\right)^3\right]^0$

a)

0

b)

1

c)

3

d)

$3x^6$

111.

Simplify the expression $\frac{2x^{-2}y^{-2}}{16x^{-12}y^2}=$ .

a)

$-24x^{14}$

b)

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

c)

$\frac{x^{10}}{8y^4}$

d)

$\frac{1}{16x^8y^4}$

112.

Which is a simplified form of the following expression using only positive exponents? $\frac{10x^{-3}}{2y^5}$

a)

$\frac{1}{5x^3y^5}$

b)

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

c)

$\frac{1}{x^3y^5}$

d)

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

113.

Which is a simplified form of the following expression using only positive exponents? $-2x^2y^{-5}z^{-7}$

a)

$\frac{1}{2x^2y^5z^7}$

b)

$\frac{y^5z^7}{-2x^2}$

c)

$\frac{-2x^2}{y^5z^7}$

d)

$\frac{-2}{x^2y^5z^7}$

114.

Which among the choices is equivalent to $\left(2x^5y^2\right)\left(4xy^3\right)+\left(x^4y^4\right)\left(3x^2y\right)$

a)

$8x^6y^5$

b)

$3x^6y^5$

c)

$11x^6y^5$

d)

$5x^6y^5$

115.

Simplify the expression: $2m^{10}n^2\left(-7m^9n^5\right)^2-\left(-m^7n^3\right)^4=$

a)

$98m^{28}n^{12}$

b)

$97m^{28}n^{12}$

c)

$96m^{28}n^{12}$

d)

$-15m^{28}n^{12}$

LAWS OF EXPONENTS (A)

Total questions: 115

Worksheet time: 38mins

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