Question 1

Which of the following is equivalent to $$\sqrt[3]{x^5$}$$ using rational exponents?

Accepted Answer

$$x^{5/3}$$

Question 2

Rewrite $$\sqrt[4]{16x^8$}$$ using rational exponents.

Accepted Answer

$$(16x^8$$)^{1/4}$

Question 3

Simplify $$\left(\dfrac{a^7$b^3$$}{$$32a^2b$$^{-7}$$}\$$right)^2$$ under the fifth root.

Accepted Answer

$$\sqrt[5]{\dfrac{a$$^{10}$$b^{20}$$}{1024}}$

Question 4

Evaluate $$16^{3/4}.$$

Accepted Answer

Question 5

Which property allows you to write $$(a^m)^n = a$$^{mn}$$?

Accepted Answer

Power of a Power Rule

Question 6

Simplify $$\dfrac{\sqrt[3]{x}}{\sqrt[5]{x}}.$$

Accepted Answer

$$x^{2/15}$$

Question 7

Express $$a^{-\frac{3}$${4}}$$ as a radical.

Accepted Answer

$$\dfrac{1}{\sqrt[4]{a^3$}}$$

Question 8

Which of the following is equivalent to $$\sqrt[4]{\dfrac{2x$$^{-1}$$w^5$$}{$$32x^7w$$}}$?

Accepted Answer

$$\dfrac{w}{2x^2$}$$

Question 9

Simplify $$\left(\dfrac{81a^5$b^{-5}$$}{$$ab^3$$}\$$right)^3$ under the fourth root.

Accepted Answer

$$\sqrt[4]{81^3$ a$$^{12}$$ b$$^{-24}$$}$$

Question 10

Which of the following is the correct application of the negative exponent rule?

Accepted Answer

$$a^{-n}$$ = \dfrac{1}{a^n}$$

Question 11

If $$a^0 = 1$, what must be true about a$?

Accepted Answer

$$a 
eq 0$$

Question 12

Which of the following is equivalent to $$\left(\sqrt[3]{x} \cdot \sqrt[4]{x}\right)$$?

Accepted Answer

$$x^{7/12}$$

Question 13

Simplify $$\left(\dfrac{a}{b}\$$right)^{m/n}$$ using radicals.

Accepted Answer

$$\dfrac{\sqrt[n]{a^m}}{\sqrt[n]{b^m}}$$

Question 14

Which of the following is the correct interpretation of $$a^{m/n}$$?

Accepted Answer

$$\sqrt[n]{a^m}$$

Question 15

If $$a^m \cdot a^n = a$$^{m+n}$$, what is a$$^{2/3}$$ \cdot a$$^{1/6}$$?

Accepted Answer

$$a^{5/6}$$

Question 16

Which of the following is equivalent to $$\sqrt{3}$$?

Accepted Answer

$$3^{1/2}$$

Question 17

Simplify $$\$$left(a^2$$b^3$$\$$right)^{1/2}$.

Accepted Answer

$$a^{1}b$$^{3/2}$

Question 18

Which of the following is the correct application of the quotient rule for exponents?

Accepted Answer

$$\dfrac{a^m}{a^n} = a$$^{m-n}$$

Question 19

A chemist needs to dilute a solution by a factor of $$\sqrt[3]{8}. $$What is the equivalent rational exponent?

Accepted Answer

$$8^{1/3}$$

Rational Exponents and Their Properties

Study Guide - Practice Questions