Free Printable Rationals and Radicals

1.

Which of the following is equivalent to

\frac{1}{a^n}

?

a)

$a^{-n}$

b)

$\sqrt{a}$

c)

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

d)

$-a^n$

2.

Which of the following is equivalent to

\frac{a^m}{a^n}

?

a)

$a^{m-n}$

b)

$\sqrt{a^m}$

c)

$a^{\frac{m}{n}}$

d)

$man$

3.

Which is equivalent to the following... ?

a)

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

b)

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

c)

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

d)

$3x^5$

4.

Which is equivalent to the following... ?

a)

$3\left(x^{\frac{5}{4}}\right)$

b)

$3\left(x^{\frac{4}{5}}\right)$

c)

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

d)

$3x^5$

5.

Which is equivalent to the following... $8^{\frac{4}{3}}$ ?

a)

16

b)

64

c)

1/16

d)

4

6.

Which is equivalent to the following... $\left(5^3\right)^2$ ?

a)

$5^6$

b)

$5^5$

c)

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

d)

$5^{32}$

7.

Which is equivalent to the following... $\left(4^{-1}\right)^2$ ?

a)

1/16

b)

-16

c)

1/8

d)

-1/16

8.

Which of the following is not equivalent to each other? (Which one is not like the others?)

a)

$x^{\frac{10}{4}}$

b)

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

c)

$x^2\sqrt{x}$

d)

$x\sqrt{x}$

9.

Solve for x. $3x^3=375$

a)

x = 5

b)

x = 3

c)

x = -5

d)

x = 25

10.

Solve for x. $\left(x-4\right)^4=256$

a)

x = 8 and x = 0

b)

x = 8

c)

x = 8 and x = -8

d)

x = 0 and x = 4

11.

Simplify the following. $\frac{1}{\left(6^{\frac{1}{3}}\cdot6^{\frac{2}{3}}\right)^{-1}}$

a)

6

b)

1/6

c)

-1/6

d)

1/216

12.

Simplify the following. $\sqrt{18}\cdot\sqrt{2}$

a)

6

b)

$\sqrt{20}$

c)

4.24264

d)

4

13.

Simplify the following.

a)

$4\sqrt{10}$

b)

$2\sqrt{10}$

c)

$16\sqrt{10}$

d)

$8\sqrt{5}$

14.

Combine the following. $4\left(5^{\frac{3}{4}}\right)-2\left(5^{\frac{3}{4}}\right)$

a)

$2\left(5^{\frac{3}{4}}\right)$

b)

$2\left(5^{\frac{6}{4}}\right)$

c)

$-2\left(5^{\frac{3}{4}}\right)$

d)

$2\left(5^{\frac{0}{4}}\right)$

15.

$\sqrt{20}+3\sqrt{5}$

a)

$5\sqrt{5}$

b)

$3\sqrt{25}$

c)

$7\sqrt{5}$

d)

$\sqrt{65}$

Rationals and Radicals

Total questions: 15

Worksheet time: 8mins

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