Free Printable Algebra 2B Rational exponents & Radicals

1.

Write in exponential form
∛x⁷

a)

x⁷∕ ³

b)

x3⁄7

c)

3x⁷

d)

7x³

2.

Write as a radical expression
y²⁄ ³

a)

2y³

b)

√y³

c)

∛y²

d)

3y²

3.

Simplify the following expression:

a)

2

b)

4

c)

16

d)

64

4.

Simplify:

a)

2

b)

4

c)

16

d)

64

5.

125^2/3

a)

5

b)

25

c)

75

d)

5

6.

Rewrite & evaluate: 4^5/2

a)

10

b)

16

c)

32

d)

64

7.

Simplify:

a)

8x⁹

b)

8x³

c)

8x⁴√x

d)

8x³√x

8.

a)

√18 + 11√2

b)

22√5

c)

11√20

d)

14√2

9.

Simplify: 2√40 - 3√10

a)

5√10

b)

√10

c)

-√30

10.

Simplify . Your answer should contain only positive exponents. $4v^{\frac{2}{3}}\cdot v^{-1}$

a)

$4v^{\frac{1}{3}}$

b)

$\frac{4}{v^{\frac{1}{3}}}$

c)

$\frac{v^{\frac{1}{3}}}{4}$

d)

$\frac{1}{4v^{\frac{1}{3}}}$

11.

Simplify . Your answer should contain only positive exponents. $\left(a^{\frac{1}{2}}b^{\frac{1}{2}}\right)^{-1}$

a)

$\frac{1}{a^{\frac{1}{2}}b^{\frac{1}{2}}}$

b)

$a^{\frac{1}{2}}b^{\frac{1}{2}}$

c)

$-\frac{1}{a^{\frac{1}{2}}b^{\frac{1}{2}}}$

d)

$-a^{\frac{1}{2}}b^{\frac{1}{2}}$

12.

Simplify . Your answer should contain only positive exponents. $\frac{2x^{\frac{1}{2}}y^{\frac{1}{3}}}{2x^{\frac{4}{3}}y^{-\frac{7}{4}}}$

a)

$\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

b)

$\frac{x^{\frac{5}{6}}}{y^{\frac{25}{12}}}$

c)

$\frac{2y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

d)

$\frac{y^{\frac{17}{12}}}{x^{\frac{5}{6}}}$

13.

Simplify . Your answer should contain only positive exponents. $u^{-\frac{5}{4}}v^2•\left(u^{\frac{3}{2}}\right)^{-\frac{3}{2}}$

a)

$\frac{v^2}{u^{\frac{7}{2}}}$

b)

$\frac{v^2}{u^{\frac{5}{2}}}$

c)

$\frac{v^2}{u^{\frac{5}{4}}}$

d)

$v^2$

14.

Rewrite the expression without using a radical:

a)

(2x+1)^3/4

b)

(2x+1)^4/3

c)

4(2x+1)³

d)

3(2x+1)⁴

15.

Rewrite in simplest radical form. . $\sqrt{20b^2}$

a)

$5\sqrt{b^2}$

b)

$10\sqrt{2b}$

c)

$2b\sqrt{5}$

d)

$20b$

16.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

17.

Simplify:

a)

2

b)

8

c)

16

d)

32

18.

Simplify:

a)

2

b)

4

c)

8

d)

16

19.

8^5/3

a)

64

b)

32

c)

16

d)

24

20.

Evaluate 81^3/4

a)

1/3

b)

3

c)

27

d)

243

21.

a)

True

b)

False

22.

Multiply then simplify: (√5)(√15)

a)

√75

b)

5√3

c)

3√5

d)

√20

23.

Multiply then simplify: 75^(1/2)*x^(1/2)

a)

5x²√3

b)

5x

c)

5x√3

d)

5√3x

24.

Rewrite in simplest radical form: (18a⁶b²)^(1/2)

a)

3a⁶b²√2

b)

3a³b²√2b

c)

3a³b√2

d)

2a³b√2

25.

Write in exponent form √x⁵

a)

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

b)

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

c)

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

d)

X⁵

26.

Simplify writing your answer with a positive exponent

a)

b)

c)

d)

27.

Simplest radical form

a)

3 x² y² z √3yz

b)

3 x y z √xy²

c)

3xyz

d)

Can't Simplify

28.

Simplify $x^{\frac{2}{3}}\cdot x^{\frac{1}{3}}$

a)

2x

b)

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

c)

x

d)

x²

29.

Simplify $\left(x^{-2}\right)^{-\frac{1}{2}}$

a)

$\frac{1}{x^{\frac{3}{2}}}$

b)

$\frac{1}{x^2}$

c)

$\frac{1}{x}$

d)

x

30.

∛k⋅∜k can be rewritten as:

a)

k^7/12

b)

k^1/12

c)

k^1/7

d)

∜k³

31.

$yx^{\frac{1}{3}}\cdot xy^{\frac{3}{2}}$

a)

$x^{\frac{4}{3}}y^{\frac{5}{2}}$

b)

$x^{\frac{2}{3}}y^{\frac{1}{2}}$

c)

$x^{\frac{1}{3}}y^{\frac{3}{2}}$

d)

$x^{\frac{2}{3}}y^{\frac{4}{3}}$

32.

Simplify . Your answer should contain only positive exponents. $\left(x^{\frac{5}{3}}y^{-2}\right)^0$

a)

$1$

b)

$\frac{x^{\frac{5}{3}}}{y^2}$

c)

$x^{\frac{5}{3}}y^2$

d)

$\frac{y^2}{x^{\frac{5}{3}}}$

33.

Combine:

500^{\frac{1}{3}}+1372^{\frac{1}{3}}

a)

$12\left(4^{\frac{1}{3}}\right)$

b)

$1872^{\frac{1}{3}}$

c)

$1872^{\frac{2}{3}}$

d)

$12\left(8^{\frac{1}{3}}\right)$

34.

Combine: $4\left(3^{\frac{1}{6}}\right)-2\left(192^{\frac{1}{6}}\right)$

a)

0

b)

$2\left(-189\right)^{\frac{1}{6}}$

c)

$-124^{\frac{1}{6}}$

d)

$-4\left(3^{\frac{1}{6}}\right)$

35.

What is the simplified form of the expression?

a)

12

b)

4

c)

2³√4

d)

24^1/3

36.

Perform the indicated operation.

a)

8∛3

b)

∛456

c)

15∛3

d)

12∛5

37.

Which is equivalent to the above expression?

a)

b)

c)

d)

38.

Simplify

a)

81a⁷

b)

3a³

c)

3a⁷

d)

81a¹²

39.

Simplify.

a)

b²

b)

10b³

c)

25b²

d)

5b²

40.

a)

A

b)

C

c)

B

d)

D

41.

$\frac{\sqrt[]{t}}{\sqrt[3]{t}}$ can be written as:

a)

t^1/6

b)

t^1/5

c)

t^1/3

d)

∜t

42.

a)

A

b)

B

c)

C

d)

D

43.

a)

A

b)

B

c)

C

d)

D

44.

a)

A

b)

B

c)

C

d)

D

45.

$\ \frac{2}{\sqrt[3]{4}}$ Rationalize.

a)

$\sqrt[3]{2}$

b)

$1$

c)

$\frac{2\sqrt[3]{4}}{4}$

d)

$\frac{\sqrt[3]{4}}{2}$

Algebra 2B Rational exponents & Radicals

Total questions: 45

Worksheet time: 1hrs 25mins

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