Free Printable Properties of Exponents Mixed Review

1.

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

2.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

3.

Select the expression that is equivalent (equal) to (7⁶)⁴.

a)

7¹⁰

b)

7²

c)

7²⁴

d)

7²⁷

4.

What is the correct way to expand $5^3\cdot5^2$ ?

a)

$\left(5+5+5\right)\left(5+5\right)$

b)

$\left(5\times3\right)\left(5\times2\right)$

c)

$\left(5\times5\right)\left(3\times2\right)$

d)

$\left(5\cdot5\cdot5\right)\left(5\cdot5\right)$

5.

Select the expression equivalent (equal) to $\frac{6^8}{6^3}$ .

a)

$6^{11}$

b)

$6^5$

c)

$6^{24}$

d)

$6^{-5}$

6.

Which expression is equivalent (equal) to $4^{12}\times7^{12}$ .

a)

$28^{24}$

b)

$21^{12}$

c)

$28^{12}$

d)

$28^{144}$

7.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

8.

Select the expressions that are equivalent (equal) to $\left(m^7\cdot m^3\right)^4$ . (There is more than one answer!)

a)

$m^{40}$

b)

$m^{28}\cdot m^{12}$

c)

$m^{11}\cdot m^7$

d)

$\left(m^{10}\right)^4$

9.

Which expression is equivalent (equal) to $\frac{10^{-3}}{10^9}$ .

a)

$10^{-12}$

b)

$10^{-6}$

c)

$10^6$

d)

$10^{-27}$

10.

Which expression is equivalent (equal) to $\frac{\left(6^{-4}\right)^{-2}}{6^2}$ .

a)

$6^6$

b)

$6^{-10}$

c)

$6^{-8}$

d)

$6^{10}$

11.

Simplify: (x⁸)(x^-5)

a)

x^-40

b)

x^-13

c)

x¹³

d)

x³

12.

Simplify the expression using the properties of exponents.
$\frac{t^{12}u^7}{t^2u}$

a)

$t^{14}u^8$

b)

$t^{24}u^7$

c)

$t^{10}u^7$

d)

$t^{10}u^6$

13.

Use the properties of exponents to write the expression as a single power: (b¹)(b¹¹)

a)

b¹¹

b)

b¹⁰

c)

b¹²

14.

4³x 4³

a)

4⁶

b)

4⁹

c)

16⁶

d)

16⁹

15.

7⁸ x 7

a)

7⁹

b)

49⁸

c)

7⁸

d)

49⁹

16.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

17.

Simplify: (3x²)³

a)

27x⁶

b)

9x⁶

c)

3x⁶

d)

9x⁵

18.

What is the exponent form for 6?

a)

6⁰

b)

6¹

c)

6×1

d)

0

19.

(-5)³

a)

-15

b)

125

c)

-125

d)

-625

20.

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

a)

0

b)

1

21.

$y^0=$

a)

y

b)

0

c)

1

d)

10

22.

$365^0=$

a)

0

b)

1

c)

365

d)

$\frac{1}{365}$

23.

$x^{-5}$ =

a)

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

b)

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

c)

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

d)

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

24.

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

25.

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

a)

$x^{12\ }$

b)

$x^{-1}$

c)

$x^7$

d)

$x^{34}$

26.

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

a)

$m^8$

b)

$m^{12}$

c)

$m^4$

d)

$m^9$

27.

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

a)

$x^6$

b)

$x^{12}$

c)

$x^{-42}$

d)

$x^{-12}$

28.

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

29.

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

a)

$x^{13}$

b)

$x^{36}$

c)

$x^5$

d)

$x^{-5}$

30.

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

a)

$x^9$

b)

$x^{25}$

c)

$x^{-9}$

d)

$x^{-25}$

31.

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

a)

$3x^2$

b)

$3x$

c)

$9x$

d)

$6x$

32.

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

a)

$a^8b^{16}$

b)

$a^2b^4$

c)

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

d)

$a^2b^{16}$

33.

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

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

34.

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

a)

$x^{14}$

b)

$x^9$

c)

$x^5$

d)

$2x^7$

35.

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

a)

$a^3b^{35}$

b)

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

c)

$a^8b^8$

d)

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

36.

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

a)

$ab^{16}$

b)

$a^8b^{16}$

c)

$a^9b^{10}$

d)

$ab^{10}$

37.

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

38.

According to exponent rules, when we divide two powers with the same base we _______ the exponents. Example: $\frac{h^8}{h^5}$

a)

add

b)

subtract

c)

multiply

d)

divide

39.

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

a)

x²

b)

x

c)

1

d)

x⁸

40.

x⁴ (x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

41.

a)

x⁴

b)

x⁸

c)

x¹²

d)

x²⁰

42.

a)

y¹⁶

b)

y³

c)

16y

d)

y⁴⁸

43.

Billy was asked to solve 3⁵∙3⁴. He got 9²⁰. What error did he make?

a)

When he multiplies exponents, he is supposed to add the base and the exponent

b)

When he multiplies exponents, he is supposed to multiply the base and keep the exponents

c)

When he multiplies exponents, he is supposed to keep the base and add the exponents if the base is the same

d)

None of the above

44.

a)

8x⁴

b)

8x⁸

c)

6x⁴

d)

6x⁸

45.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

46.

a)

b)

c)

d)

47.

a)

b)

c)

d)

48.

a)

b)

c)

d)

49.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

50.

Write with positive exponents:

1/a^-2

a)

a^-2

b)

a²

c)

1/a¹

51.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

52.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

53.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

54.

Simplify

a)

x⁴/3

b)

3x¹⁰

c)

36x¹⁰

d)

3x⁴

55.

a)

2 / x²

b)

-2x²

c)

2x²

d)

2x¹⁴

56.

(2m³)(3m⁴) =

a)

5m⁷

b)

6m¹²

c)

5m¹²

d)

6m⁷

57.

a)

-30a²⁰c

b)

7a¹³b⁵c

c)

7a²⁰c

d)

-30a¹³b⁵c

58.

a)

b)

16c³d³

c)

d)

59.

a)

b)

c)

3x⁴y

d)

60.

a)

x⁷

b)

x¹¹

c)

d)

61.

a)

b)

2x²z⁴

c)

3x²y⁵z⁴

d)

62.

a)

3ab⁸c³

b)

c)

d)

2ab⁸c¹¹

63.

a)

b)

-12x²y

c)

d)

-108xy²

64.

a)

b)

c)

d)

65.

a)

$25x^{22}$

b)

$10x^{22}$

c)

$25x^{13}$

d)

$-25x^{22}$

66.

a)

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

b)

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

c)

$27x^8yz^4$

d)

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

67.

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)

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

68.

Simplify the expression using the properties of exponents.

$\frac{21x^7}{3x^4}$

a)

$7x^3$

b)

$3x^3$

c)

$7x^{11}$

d)

$18x^3$

69.

Simplify the expression using the properties of exponents.
$\frac{t^{12}u^7}{t^2u}$

a)

$t^{14}u^8$

b)

$t^{24}u^7$

c)

$t^{10}u^7$

d)

$t^{10}u^6$

70.

Simplify: (x⁸)(x^-5)

a)

x^-40

b)

x^-13

c)

x¹³

d)

x³

71.

Select the expressions that are equivalent (equal) to $\left(m^7\cdot m^3\right)^4$ . (There is more than one answer!)

a)

$m^{40}$

b)

$m^{28}\cdot m^{12}$

c)

$m^{11}\cdot m^7$

d)

$\left(m^{10}\right)^4$

Properties of Exponents Mixed Review

Total questions: 71

Worksheet time: 9hrs 45mins

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