Free Printable Exponent Rules Review

1.

$10\times10\times10\times10\times10=$

a)

$10\times5$

b)

$10^5$

2.

$10^3=$

a)

$10\times10\times10$

b)

$10\times3$

c)

$10+10+10$

d)

10,000

3.

Which number is the BASE? $2^7$ =128

a)

2

b)

7

c)

128

d)

$2^7$

4.

If a number or variable does not have an exponent, we can assume the exponent is:

a)

0

b)

1

5.

$y^0=$

a)

y

b)

0

c)

1

d)

10

6.

$365^0=$

a)

0

b)

1

c)

365

d)

$\frac{1}{365}$

7.

$x^{-5}$ =

a)

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

b)

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

c)

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

d)

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

8.

The product rule says that when you are multiplying two exponents with the same base, you keep the base and ________ the exponents

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

9.

$x^3\cdot x^4\ =$

a)

$x^{12\ }$

b)

$x^{-1}$

c)

$x^7$

d)

$x^{34}$

10.

$m^2\cdot m^6\cdot m=$

a)

$m^8$

b)

$m^{12}$

c)

$m^4$

d)

$m^9$

11.

$x^{-3}\cdot x^7\cdot x^2$ =

a)

$x^6$

b)

$x^{12}$

c)

$x^{-42}$

d)

$x^{-12}$

12.

The quotient rule says that when you are dividing two exponents with the same base, you keep the base and __________ the exponents.

a)

Add

b)

Subract

c)

Multiply

d)

Divide

13.

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

a)

$x^{13}$

b)

$x^{36}$

c)

$x^5$

d)

$x^{-5}$

14.

$\frac{x^{17}}{x^8}$

a)

$x^9$

b)

$x^{25}$

c)

$x^{-9}$

d)

$x^{-25}$

15.

$\frac{9x^2}{3x^{ }}=$

a)

$3x^2$

b)

$3x$

c)

$9x$

d)

$6x$

16.

$\frac{a^5b^{10}}{a^3b^6}=$

a)

$a^8b^{16}$

b)

$a^2b^4$

c)

$a^{15}b^{60}$

d)

$a^2b^{16}$

17.

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

The power of a power rule says that when an exponential expression is raised to a power (as shown above), you should _________ the inner and outer exponents

a)

add

b)

subtract

c)

multiply

d)

divide

18.

$\left(x^7\right)^2$ =

a)

$x^{14}$

b)

$x^9$

c)

$x^5$

d)

$2x^7$

19.

$\left(a^3b^5\right)^7$ =

a)

$a^3b^{35}$

b)

$a^{10}b^{12}$

c)

$a^8b^8$

d)

$a^{21}b^{35}$

20.

$\left(ab^2\right)^8$ =

a)

$ab^{16}$

b)

$a^8b^{16}$

c)

$a^9b^{10}$

d)

$ab^{10}$

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: x¹⁰⋅x⁴

a)

x⁴⁰

b)

x¹⁴

c)

x⁶

d)

2x¹⁴

26.

Simplify: x⁸/x²

a)

x¹⁶

b)

x⁴

c)

x⁵

d)

x⁶

27.

Simplify: 7p⁰

a)

7

b)

1

c)

simplified

d)

7p

28.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

29.

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

30.

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

31.

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

32.

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

a)

(-2)⁹

b)

(-2)¹⁸

c)

(-2)⁻³

d)

(-2)

33.

Simplify using your exponent rule(s) x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

34.

True or False?

a)

True

b)

False

35.

Can you leave a negative exponent in your answer?

a)

YES

b)

NO

36.

Simplify: $6^5\cdot6^2$

a)

$6^7$

b)

$6^3$

c)

$36^7$

d)

$6^{10}$

37.

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

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

38.

$3^7\cdot3^7$

a)

$9^{49}$

b)

$3^{14}$

c)

$3^{49}$

d)

$9^{14}$

39.

Simplify: $10x^8\cdot9x$

a)

$90x^8$

b)

$19x^9$

c)

$90x^9$

d)

$19x^9$

40.

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

a)

$1^3$

b)

$0^3$

c)

$2^3$

d)

$2^{15}$

41.

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)

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

42.

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

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$3x^{30}$

43.

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

a)

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

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

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

44.

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

a)

$10m^5$

b)

$2^5m^5$

c)

$25m^5$

d)

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

45.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

46.

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

a)

$5x^4$

b)

$-5x^4$

c)

$5x^3$

d)

$-5x^3$

47.

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

a)

$5k^2$

b)

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

c)

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

d)

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

48.

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

a)

$6k^8$

b)

$-6k^{15}$

c)

$6k^{15}$

d)

$-6k^8$

49.

$4n^2\ \cdot\ n$

a)

$4n^3$

b)

$4n$

c)

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

d)

$\frac{4}{n}$

50.

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

a)

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

b)

$\frac{3}{7}$

c)

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

d)

$0.4285$

51.

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

a)

$9x^3$

b)

$x^3$

c)

$27x^3$

d)

$6x^3$

52.

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

a)

$35x^3$

b)

$35x^4$

c)

$2x^3$

d)

$35x^2$

53.

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

a)

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

b)

$\frac{7a}{3}$

c)

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

d)

$\frac{3}{7a}$

54.

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

a)

$63x^5$

b)

$13x^4$

c)

$24x^4$

d)

$36x^2$

55.

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

a)

$10b^6$

b)

$21b^6$

c)

$10b^5$

d)

$21b^5$

56.

When using the Power to a Power rule, what are you supposed to do with the exponents? ex. $\left(x^9\right)^{12}$

a)

Add the exponents.

b)

Multiply the exponents.

c)

Subtract the exponents.

d)

Make it $12x^9$

57.

The Quotient of Powers Property says, "to divide powers with the same base, _________ the exponents."

ex.

\frac{\text{}y^6}{\text{}y^3}

a)

Divide

b)

Add

c)

Multiply

d)

Subtract

58.

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

a)

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

b)

$4v^2$

c)

$-6v^8$

d)

$6v^8$

59.

Anything raised to the zero power (except zero) is equal to what?

(a)

60.

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

a)

$2v^4$

b)

$8v^3$

c)

$2^2v^4$

d)

$8v^4$

61.

Simplify the following
(no negative exponents):
$\frac{\left(-14\right)^6}{\left(-14\right)^9}$

a)

$\left(-14\right)^{-3}$

b)

$\frac{1}{\left(-14\right)^{15}}$

c)

$\frac{1}{\left(-14\right)^3}$

d)

$\left(-14\right)^{54}$

62.

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)

$-6cd^3$

63.

What is the value of 100⁰?

a)

1

b)

0

c)

100

64.

What is the exponent form for
6?

a)

6⁰

b)

6¹

c)

6×1

d)

0

65.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

66.

a)

x^1/2

b)

x³

c)

x²

d)

x^-2

67.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

68.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

69.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

70.

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

a)

add

b)

subtract

c)

multiply

d)

divide

71.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

72.

Simplify 4^-2=

a)

1/16

b)

-16

c)

1/4

d)

-42

73.

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

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

74.

a)

b)

c)

d)

75.

Which is equivalent to 5 x 5 x 5 x 5

a)

5³

b)

5⁴

c)

4⁵

d)

5⁵

76.

Which is equivalent to 2⁴

a)

8

b)

20

c)

16

d)

12

77.

The exponent equivalent of 20 x 20 x 20 is:

a)

20 x 3

b)

20³

c)

3²⁰

d)

2000

78.

Which number is the EXPONENT?
4^{2 =}16

a)

4

b)

2

c)

16

d)

not here

79.

Simplify (2⁴)(2⁵)

a)

2²⁰

b)

4⁹

c)

4²⁰

d)

2⁹

80.

Simplify (6x⁷)²

a)

12x¹⁴

b)

36x¹⁴

c)

6x¹⁴

d)

6x⁹

81.

a)

1³

b)

4³

c)

1^1.6

d)

4^1.6

82.

Simplify the expression x⁵x⁷

a)

x³⁵

b)

x¹²

c)

x²

d)

x^-2

83.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

84.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

85.

Simplify
x⁴⋅x³⋅x

a)

x⁸

b)

x¹²

c)

x⁷

d)

x¹⁰

86.

Simplify
(x²)³

a)

x³

b)

x⁵

c)

x⁶

d)

x⁴

87.

Simplify
y⁸⋅y³

a)

y²⁴

b)

y¹¹

c)

y⁵

d)

y¹⁵

88.

Expand
(xy)³

a)

x⋅x⋅x⋅y

b)

xy⋅xy⋅xy

c)

x⋅y⋅y⋅y

d)

3x⋅3y

89.

Simplify
(y³)⁴

a)

y⁷

b)

y¹²

c)

y^-1

d)

y⁸

90.

Simplify

a)

y²

b)

y³⁵

c)

y¹²

d)

y¹⁴

91.

Simplify

a)

x¹²

b)

x¹⁷

c)

x⁶

d)

x²³

92.

Simplify

a)

z

b)

z¹²

c)

1

d)

z¹⁴

93.

Expand
x⁵

a)

x

b)

x⋅x⋅x

c)

x⋅x⋅x⋅x⋅x

d)

x⋅x

94.

Simplify

a)

z¹⁵

b)

z⁸

c)

z³

d)

z¹¹

95.

Expand fully.
(x²)³

a)

x⋅x⋅x

b)

x²⋅x²⋅x²

c)

x⋅x⋅x⋅x⋅x⋅x

d)

x⋅x⋅x⋅x⋅x

96.

Simplify
(z⁴)³⋅z⁴

a)

z¹¹

b)

z¹⁶

c)

z⁵

d)

z²⁸

Exponent Rules Review

Total questions: 96

Worksheet time: 3hrs 12mins

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