Free Printable Properties of Exponents

1.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

2.

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

a)

add

b)

subtract

c)

multiply

d)

divide

3.

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

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

4.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

5.

Simplify (evaluate):

3^-3

a)

-27

b)

-9

c)

-1/9

d)

1/27

6.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same value

d)

Zero is greater

7.

(3⁴)(3⁷)

a)

3²⁸

b)

3³

c)

3^-3

d)

3¹¹

8.

(x⁸)(x^-5)

a)

x^-40

b)

x^-13

c)

x¹³

d)

x³

9.

(5⁸) / (5³)

a)

5⁵

b)

1⁵

c)

5¹¹

d)

1¹¹

10.

(8⁵)³

a)

8⁸

b)

8¹⁵

c)

8²

d)

1/8²

11.

(t^-6)^-5

a)

t^-11

b)

t^-30

c)

t³⁰

d)

t¹¹

12.

Express as a positive exponent: 4^-8

a)

1⁸/4

b)

4⁸/1

c)

4/1⁸

d)

1/4⁸

13.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

14.

8⁷ ⁄ 8²

a)

8⁵

b)

8⁹

c)

8¹⁴

d)

1⁵

15.

$x^{12\ \ }\ \div\ \ \ x^{-12}$

a)

$x^0$

b)

$x^{12}$

c)

$x^{24}$

d)

$x^{-24}$

16.

$\left(k^2\right)^5$

a)

k⁷

b)

k³

c)

$\frac{1}{k^{10}}$

d)

k¹⁰

17.

$b^7\ \div\ b$

a)

b⁶

b)

b⁷

c)

b¹

d)

b^-6

18.

Check all that apply. $11^{-2}$

a)

b)

c)

d)

19.

25⁸ x 3⁸

a)

75¹⁶

b)

75⁸

c)

25⁸

d)

3⁸

20.

-64³ / 8³

a)

-8³

b)

16³

c)

8³

d)

8³

21.

13¹² x 15¹²

a)

195¹²

b)

28²⁴

c)

15¹²

d)

195²⁴

22.

a)

w^-3

b)

w³

c)

w²

d)

w^-13

23.

$x^{-3}\ \div\ x^{-9}$

a)

x¹²

b)

x⁶

c)

x^-6

d)

x^-12

24.

$5^6\cdot5^9$

a)

5

b)

$5^{54}$

c)

$25^{15}$

d)

$5^{15}$

25.

$5^3\cdot7^3$

a)

$35^9$

b)

$7^6$

c)

$35^3$

d)

$5^6$

26.

$7^{-3}$

a)

-343

b)

$\frac{1}{7^3}$

c)

343

d)

$\frac{1}{7^{-3}}$

27.

$m\cdot m^3$

a)

$m^2$

b)

$m^3$

c)

2m

d)

$m^4$

28.

24 x 24^-5

a)

24^-5

b)

24^-4

c)

24^-6

d)

24

29.

(8¹²)¹²

a)

8¹²

b)

8²⁴

c)

8

d)

8¹⁴⁴

30.

x^m $\cdot$ xⁿ

a)

x^mn

b)

x^m+n

c)

x^m-n

d)

x

31.

x^m / xⁿ

a)

x^mn

b)

x^m+n

c)

x^m-n

d)

x

32.

(x^m)ⁿ

a)

x^mn

b)

x^m+n

c)

x^m-n

d)

x

33.

(12x³y)²

a)

24x⁶y²

b)

144x⁵y³

c)

144x⁶y²

d)

24x⁵y³

34.

Simplify
(3x³y⁵)⁴

a)

3x¹²y²⁰

b)

81x¹²y²⁰

c)

12x¹²y²⁰

d)

81x⁷y⁹

35.

Which expression is equivalent to: (check all that apply)

$10^{-3}\ \div\ 10^9$

a)

10^-12

b)

10^-6

c)

1/10⁶

d)

1/10¹²

36.

Simplify: (3x²)³

a)

27x⁶

b)

9x⁶

c)

3x⁶

d)

9x⁵

37.

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

a)

$28^{24}$

b)

$21^{12}$

c)

$28^{12}$

d)

$28^{144}$

38.

Simplify the following expression (check all that apply):

$\left(3^{-2}\right)^3$

a)

$\frac{1}{3^6}$

b)

$3^{-6}$

c)

$\frac{1}{3^{-6}}$

d)

$3^{-5}$

Properties of Exponents

Total questions: 38

Worksheet time: 2hrs 30mins

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