Free Printable Alg2-Simplifying Rational Exponents Practice 3

1.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

2.

Re-write $\left(5xy\right)^{-\frac{1}{3}}$ in radical form.

a)

$\ ^3\sqrt{5xy}$

b)

$\frac{1}{\ ^3\sqrt{5xy}}$

c)

$\frac{1}{\left(5xy\right)^3}$

d)

$\frac{5}{\ ^3\sqrt{xy}}$

3.

Write each expression in exponential form.

a)

A

b)

B

c)

C

d)

D

4.

Which of the following radical expressions is equivalent to $-16^{\frac{2}{3}}$

a)

b)

c)

d)

5.

Rewrite as a rational exponent

a)

7²

b)

$7^{\frac{1}{2\ }}$

c)

$7^{-2}$

d)

$7^{-\frac{1}{2}}$

6.

a)

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

b)

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

c)

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

d)

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

7.

a)

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

b)

$-2^{\frac{3}{5}}$

c)

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

d)

$8^5$

8.

a)

$5x^{\frac{5}{4}}$

b)

$5x^{-\frac{5}{4}}$

c)

$\left(5x\right)^{-\frac{5}{4}}$

d)

$\left(5x\right)^{-\frac{4}{5}}$

9.

a)

$\left(5x\right)^{-\frac{2}{1}}$

b)

$\left(5x\right)^{\frac{2}{1}}$

c)

$\left(5x\right)^{-\frac{1}{2}}$

d)

$\left(5x\right)^{\frac{1}{2}}$

10.

a)

$\left(6v\right)^3$

b)

$6v^{\frac{3}{2}}$

c)

$\left(6v\right)^{\frac{3}{2}}$

d)

$\left(6v\right)^{\frac{2}{3}}$

11.

Write each expression in exponential form.

a)

A

b)

B

c)

C

d)

D

12.

a)

A

b)

B

c)

C

d)

D

13.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

14.

Re-write $\ ^5\sqrt{\sqrt{a}}$ in rational exponent form.

a)

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

b)

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

c)

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

d)

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

15.

Rewrite the following as a radical. Simplify if possible.

a)

A

b)

B

c)

C

d)

D

16.

Write the expression in exponential form.

a)

A

b)

B

c)

C

d)

D

17.

Rewrite in radical form.

a)

A

b)

B

c)

C

d)

D

18.

Rewrite in radical form.

a)

A

b)

B

c)

C

d)

D

19.

If an exponent is not written, what is automatically the power?

a)

0

b)

1

c)

2

d)

there is no power

20.

If the index is not written in a radical problem, it is automatically what value?

a)

0

b)

1

c)

2

d)

it does not exist

21.

Simplify:

a)

2

b)

8

c)

16

d)

32

22.

8^5/3

a)

64

b)

32

c)

16

d)

24

23.

Simplify, write your answer with rational exponents.

\frac{x^{\frac{1}{2}}y^{\frac{2}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{3}}}

a)

$x^{\frac{1}{4}}y^{\frac{1}{3}}$

b)

$x^{\frac{3}{4}}y^{\frac{1}{3}}$

c)

$\frac{y^{\frac{1}{3}}}{x^{\frac{1}{4}}}$

d)

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

24.

Simplify. Write your final answer using only exponents.

\ \ ^4\sqrt{x^8y^{12}}

a)

$x^2y^3$

b)

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

c)

$x^{\frac{1}{4}}y^{\frac{1}{8}}$

d)

$x^4y^8$

25.

Simplify. Write your final answer using only exponents.

x^{\frac{4}{5}}x^{\frac{3}{5}}

a)

$x^{\frac{7}{5}}$

b)

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

c)

$x^{\frac{12}{25}}$

d)

$x^{\frac{12}{5}}$

26.

Simplify. Write your answer using only exponents. $\left(x^{\frac{4}{5}}y^{\frac{1}{4}}\right)^{\frac{2}{3}}$

a)

$x^{\frac{8}{15}}y^{\frac{1}{6}}$

b)

$x^{\frac{8}{5}}y^{\frac{1}{2}}$

c)

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

d)

$x^{\frac{22}{15}}y^{\frac{11}{12}}$

27.

Simplify. Write your answer in radical form. $\frac{y^{\frac{4}{7}}}{y^{\frac{6}{7}}}$

a)

$\frac{1}{^7\sqrt{y^2}}$

b)

$^7\sqrt{y^2}$

c)

$\frac{1}{^2\sqrt{y^7}}$

d)

$-^2\sqrt{y^7}$

28.

Simplify. Write your answer with only exponents. $\left(\frac{x^{20}}{y^{24}}\right)^{\frac{3}{4}}$

a)

$\frac{x^{15}}{y^{18}}$

b)

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

c)

$\frac{x^{\frac{83}{4}}}{y^{\frac{99}{4}}}$

d)

$\frac{x^{60}}{y^{72}}$

29.

Simplify. Write your answer with only exponents.

x^{\frac{3}{8}}x^{\frac{1}{2}}

a)

$x^{\frac{7}{8}}$

b)

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

c)

$x^{\frac{3}{10}}$

d)

$x^{\frac{3}{16}}$

30.

Write the expression using a rational exponent.

a)

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

b)

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

c)

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

d)

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

31.

Write the expression using a rational exponent.

a)

$\frac{5}{3}$

b)

$\frac{3}{5}$

c)

$10^6$

d)

$10^{\frac{1}{6}}$

32.

Write the expression using a radical.

a)

$25\sqrt{x}$

b)

$\sqrt{25x^2}$

c)

$\sqrt{5x}$

d)

$\sqrt{25x}$

33.

Write the expression in exponential form

a)

b)

c)

d)

34.

Write the expression in exponential form

a)

b)

c)

d)

35.

Write the expression in exponential form

a)

b)

c)

d)

36.

Write the expression in exponential form

a)

b)

c)

d)

37.

Write the expression in exponential form

a)

b)

c)

d)

38.

Write the expression in exponential form

a)

b)

c)

d)

39.

Write the expression in exponential form

a)

b)

c)

d)

40.

What is the rational exponent form of the following?

a)

$y^{\frac{10}{5}}$

b)

$10^{\frac{y}{5}}$

c)

$10^{\frac{5}{y}}$

d)

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

41.

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)

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

42.

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)

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

43.

Simplify . Your answer should contain only positive exponents. $\frac{a^2b^0}{3a^4}$

a)

$1$

b)

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

c)

$\frac{a^2}{3a^4}$

d)

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

44.

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)

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

45.

Simplify . Your answer should contain only positive exponents. $\left(x^0y^{\frac{1}{3}}\right)^{\frac{3}{2}}x^0$

a)

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

b)

$1$

c)

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

d)

$0$

46.

Simplify . Your answer should contain only positive exponents. $\frac{\left(m^2n^{\frac{1}{2}}\right)^0}{n^{\frac{3}{4}}}$

a)

$1$

b)

$n^{\frac{3}{4}}$

c)

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

d)

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

47.

Simplify . Your answer should contain only positive exponents. $\left(6b\right)^{\frac{-4}{3}}$

a)

$\frac{1}{6^{\frac{4}{3}}b^{\frac{4}{3}}}$

b)

$\frac{6}{b^{\frac{4}{3}}}$

c)

$\frac{b^{\frac{4}{3}}}{6}$

d)

$\frac{6^{\frac{4}{3}}}{b^{\frac{4}{3}}}$

48.

a)

y²z¹⁰√xy

b)

20yz√xy

c)

xy²z¹⁰√y

d)

yz⁶√xy²z²

49.

Simplify

√45n³

a)

3n√5n

b)

4n√8

c)

4n√-8

d)

10√n

50.

Simplify the radical...

√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

51.

√45x⁴y⁷

a)

3x²y³√5

b)

9x²y³√5y

c)

3x²y³√5y

d)

3x⁴y⁷

52.

a)

y²z¹⁰√xy

b)

20yz√xy

c)

xy²z¹⁰√y

d)

yz⁶√xy²z²

53.

√45x⁴y⁷

a)

3x²y³√5

b)

9x²y³√5y

c)

3x²y³√5y

d)

3x⁴y⁷

54.

a)

A

b)

B

c)

C

d)

D

55.

a)

xy√y

b)

x²y²√y

c)

xy√xy

d)

2x2y√y

56.

a)

A

b)

B

c)

C

d)

D

57.

a)

A

b)

B

c)

C

d)

D

58.

a)

A

b)

B

c)

C

d)

D

59.

a)

a

b)

b

c)

c

d)

d

60.

a)

a

b)

b

c)

c

d)

d

61.

a)

A

b)

B

c)

C

d)

D

62.

a)

A

b)

B

c)

C

d)

D

63.

a)

A

b)

B

c)

C

d)

D

64.

a)

A

b)

B

c)

C

d)

D

65.

a)

A

b)

B

c)

C

d)

D

66.

a)

A

b)

B

c)

C

d)

D

67.

a)

A

b)

B

c)

C

d)

D

68.

a)

A

b)

B

c)

C

d)

D

69.

a)

A

b)

B

c)

C

d)

D

70.

a)

A

b)

B

c)

C

d)

D

71.

a)

A

b)

B

c)

C

d)

D

Alg2-Simplifying Rational Exponents Practice 3

Total questions: 71

Worksheet time: 3hrs 25mins

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