Free Printable Roots and Powers

1.

Simplify: √28

a)

7√2

b)

7√4

c)

4√7

d)

2√7

2.

Simplify: √45

a)

3√5

b)

5√3

c)

9√5

d)

5√9

3.

Simplify: √196

a)

2√49

b)

14

c)

7

d)

2√98

4.

Simplify: √48

a)

4√2

b)

6√3

c)

4√3

d)

4√2

5.

Simplify 4√75

a)

4√5

b)

12√5

c)

20√3

d)

7√3

6.

Simplify √18

a)

3√2

b)

9√2

c)

3√9

d)

2√3

7.

Simplify: √200

a)

10√2

b)

2√10

c)

50√2

d)

2√50

8.

Simplify: 3√16

a)

12

b)

48

c)

√12

d)

3√4

9.

Simplify:
√(a²)

a)

a

b)

a²

c)

a^.5

d)

already simplified

10.

Simplify: √20a²

a)

2a√5

b)

4a√5

c)

5a√2

d)

2a²√5

11.

√100y⁴

a)

10√y²

b)

10y√y

c)

10y

d)

10y²

12.

Simplify: √(49x³)

a)

7x²√x

b)

7x√x

c)

7√x³

d)

7x

13.

The number under the radical sign or square root sign is called the ______.

a)

radical sign

b)

radicand

c)

factor

d)

exponent

14.

Simplify the following radical: 2√24

a)

4√6

b)

2√6

c)

24√2

d)

4√4

15.

a)

xy√y

b)

x²y²√y

c)

xy√xy

d)

2x2y√y

16.

a)

x³√x

b)

7x√x²

c)

x⁶√x

d)

√x

17.

a)

x⁴y⁴√y

b)

72xy

c)

xy√y

d)

x²y³√x²

18.

a)

y²z¹⁰√xy

b)

20yz√xy

c)

xy²z¹⁰√y

d)

yz⁶√xy²z²

19.

Express the following in simplest radical form:

$\sqrt{a^{32}}$

a)

$a^{16}$

b)

$a^8$

c)

$a^2\sqrt{a^{16}}$

d)

$a^4\sqrt{a^8}$

20.

Express the following in simplest radical form:

$\sqrt{16a^{12}}$

a)

$4a^6$

b)

$8a^6$

c)

$4\sqrt{a^{12}}$

d)

$4a^6\sqrt{2a^{ }}$

21.

Express the following in simplest radical form:

$\sqrt{75a^{11}}$

a)

$5a^5\sqrt{3a}$

b)

$25a^5\sqrt{3a}$

c)

$5a^5\sqrt{15a^3}$

d)

$25a^{10}\sqrt{3a}$

22.

Simplify $\sqrt{50x^4}$

a)

$25x^2\sqrt{2}$

b)

$5x\sqrt{2}$

c)

$25x^2$

d)

$5x^2\sqrt{2}$

23.

Simplify:

a)

8x⁹

b)

8x³

c)

$8x^4\ \sqrt[]{x}$

d)

$8x^3\ \sqrt[]{x}$

24.

Simplify

$\sqrt[]{45n^3}$

a)

$3n\ \sqrt[]{5n}$

b)

$4n\ \sqrt[]{8}$

c)

$4n\ \sqrt[]{-8}$

d)

$10\ \sqrt[]{n}$

25.

Simplify $\sqrt{18x^6y^{10}z^{14}}$

a)

$3x^3y^5z^7\sqrt{2}$

b)

$9x^2y^8\sqrt{z^{12}}$

c)

$9x^3y^5z^7\sqrt{2}$

26.

Simplify $\sqrt{40a^3b^2c^{11}}$

a)

$8abc^5\sqrt{5ac}$

b)

$2a^2bc^5\sqrt{10a}$

c)

$2abc^5\sqrt{10ac}$

27.

Rewrite in rational exponent form

a)

4^4/3

b)

4^3/4

c)

2^4/3

d)

2^3/4

28.

Rewrite in rational exponent form

a)

2^3/5

b)

-2^3/5

c)

2^5/3

d)

8⁵

29.

Simplify: y^3/8 y^1/8

a)

y^1/2

b)

y^2/8

c)

y^3/8

d)

y^5/8

30.

a)

b)

c)

31.

Simplify writing your answer with a positive exponent

a)

b)

c)

d)

32.

Write in exponential form
√x⁵

a)

X¹∕ ⁵

b)

X ²⁄⁵

c)

X⁵⁄ ²

d)

X⁵

33.

Write as a radical expression
y²⁄ ³

a)

2y³

b)

√y³

c)

∛y²

d)

3y²

34.

Simplify
x²⁄ ³⋅x¹⁄ ³

a)

2x

b)

x²⁄₉

c)

x

d)

x²

35.

Simplify
(x²⁄ ³)²⁄ ⁵

a)

x⁴∕ ¹⁵

b)

x¹⁶∕ ¹⁵

c)

x⁶

d)

6x

36.

Simplify:

a)

2

b)

8

c)

16

d)

32

37.

Simplify the following expression:

a)

16

b)

32

c)

40

d)

64

38.

Rewrite the following

∛x⁵

a)

x^3/5

b)

x^5/3

c)

x²

d)

x³⋅x⁵

39.

Which expression with a fractional exponent best represents √7 ?

a)

7^½

b)

7¼

c)

7⅓

d)

2⁷

40.

Evaluate:

a)

2

b)

4

c)

16

d)

64

41.

Simplify (evaluate):

3^-3

a)

-27

b)

-9

c)

-1/9

d)

1/27

42.

Write this expression using positive exponent:

x^-7

a)

-7

b)

-7x

c)

1/x⁷

d)

-1/x⁷

43.

Simplify (evaluate):

5^-2

a)

-10

b)

1/25

c)

1/(5)²

d)

-1/10

44.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

45.

Simplify 3a^-1c^-5/ d⁰

a)

1

b)

3/ac⁵

c)

3a/c⁵

d)

1/3a¹c⁵d

46.

Write with positive exponents:

a)

a^-2

b)

a²

c)

1/a¹

47.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

48.

Simplify.
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

49.

$\left(a^{-3}b^4c\right)^{-2}$

a)

$\frac{c^2}{a^6b^8}$

b)

$\frac{b^8}{a^6c^2}$

c)

$\frac{a^6}{b^8c^2}$

50.

$-12m^4n^{-3}p^{-2}$

a)

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

b)

$\frac{-12}{m^4n^4p^2}$

c)

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

d)

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

51.

$\left(j^{-1}k\right)^{-3}\cdot\left(j^{-5}k^4\right)^2$

a)

$\frac{k^5}{j^7}$

b)

$\frac{j^7}{k^5}$

c)

$j^{13}k^{11}$

d)

$j^7k^5$

52.

$\frac{d^{-4}}{\left(a^{-6}b^3\right)^3}$

a)

$\frac{a^{18}b^9}{d^4}$

b)

$\frac{d^4}{a^{18}b^9}$

c)

$\frac{a^{18}}{b^9d^4}$

53.

$\left(\frac{x^{-4}y^6}{z^2}\right)^{-3}$

a)

$\frac{x^{12}z^6}{y^{18}}$

b)

$\frac{y^{18}}{x^{12}z^6}$

c)

$\frac{z^6}{x^{12}y^{18}}$

d)

$\frac{x^{12}}{z^6y^{18}}$

54.

Rewrite using a positive exponent.
(-5)^-4

a)

(-5)⁴

b)

¹/_(-5)^-4

c)

¹/_(-5)⁴

d)

-625

55.

Simplify. Use positive exponents. (2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

Roots and Powers

Total questions: 55

Worksheet time: 2hrs 25mins

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