Free Printable Powers, Exponents, and Roots

1.

To find the square root of a number, you must divide it by 2.

a)

True

b)

False

2.

∛216

a)

6

b)

72

c)

108

d)

4

3.

What is the cube root of 125?

a)

5

b)

-5

c)

25

d)

-25

4.

Mr. Jarowski is hanging a square picture frame that has ab area of 169 cm². Find the side length of the frame.

a)

12 cm

b)

13 cm

c)

13 in

d)

16 cm

5.

The area of the square pool on Mr. Carr's vacation was 256 ft². How long was one side of the pool?

a)

17 ft

b)

18 ft

c)

16 ft

d)

15 ft

6.

√196 = ______

a)

14

b)

14²

c)

15

d)

15²

7.

What is 11 squared?

11²

a)

132

b)

144

c)

121

d)

22

8.

True or false? 9² is 18

a)

True

b)

False

9.

-√144

a)

12

b)

13

c)

-12

d)

None of the above

10.

$-6^2$ = ?

a)

36

b)

-36

c)

12

d)

-12

11.

$\sqrt{\left(\frac{16}{81}\right)}\ \ =\ ?$

a)

$\frac{8}{27}$

b)

$\frac{8}{9}$

c)

$\frac{4}{9}$

d)

$\frac{4}{3}$

12.

x² = 121
What does x equal? Select all that apply.

a)

121²

b)

-11

c)

11

d)

14,641

13.

Select ALL the square roots of 64

a)

4

b)

-4

c)

8

d)

-8

e)

No real roots

14.

$23^3$ means

a)

23 + 23 + 23

b)

23 x 3

c)

23 x 23 x 23

d)

3 + 23

15.

k⁴ * k²

a)

k²

b)

k⁶

c)

k⁸

16.

(-9)⁵*(-9)³=

a)

(-9)⁸

b)

(-9)²

c)

(-9)¹⁵

17.

$\frac{f^7}{f^3}$ =

a)

$f^{10}$

b)

$f^4$

c)

$f^{21}$

18.

$\frac{-3^9}{-3^3}$

a)

$-6^6$

b)

$-3^6$

c)

$-3^{12}$

19.

$\left(b^6\right)^2$

a)

$b^{12}$

b)

$b^4$

c)

$b^8$

20.

$\left(p^3\right)^2$

a)

$p^5$

b)

$p^6$

c)

$p^1$

21.

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

a)

$5^{15}$

b)

$5^2$

c)

$5^8$

22.

Which rule would you use?

g^6\cdot g^7

a)

Product Property

b)

Quotient Property

c)

Power to Power

23.

Which rule would you use?

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

a)

Product Property

b)

Quotient Property

c)

Power to Power

24.

Which rule would you use?

\left(r^3\right)^2

a)

Multiplication Property

b)

Quotient Property

c)

Power to Power

25.

5², in this example, 5 is the ______ and 2 is the _______

a)

base, product

b)

exponent, base

c)

base, exponent

d)

product, base

26.

Write the product as a power :

(-2) ⋅ (-2) ⋅ (-2) ⋅ (-2) ⋅ (-2)

a)

-2⁵

b)

2^-5

c)

(-2)⁵

d)

(-2)^-5

27.

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

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

28.

2 * 2² *2²

a)

2⁴

b)

8⁴

c)

36

d)

2⁵

29.

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

30.

Simplify: $\frac{m^{10}}{m^2}$

a)

$m^{20}$

b)

$m^{12}$

c)

$m^8$

d)

$m^5$

31.

What does the term "squared" mean?

a)

raised to the power of 3

b)

raised to the power of 4

c)

raised to the power of 2

32.

What does the term"cubed" mean?

a)

raised to the power of 2

b)

raised to the power of 3

c)

raised to the power of 4

33.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

34.

(5²)³

a)

5⁶

b)

5⁵

c)

5⁷

d)

5⁸

35.

9⁴ x 9^x = 9⁸

a)

x = 4

b)

x = 2

c)

x = -4

d)

x = -2

36.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

37.

Simplify (6x⁷)²

a)

12x¹⁴

b)

36x¹⁴

c)

6x¹⁴

d)

6x⁹

Powers, Exponents, and Roots

Total questions: 37

Worksheet time: 1hrs 2mins

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