Question 1

Which of the following is equivalent to $$\sqrt[3]{x^6$}$$ for all real $$x$$?

Accepted Answer

$$|x^2$|$$

Question 2

Simplify the expression $$\sqrt{50}.$$

Accepted Answer

$$5\sqrt{2}$$

Question 3

Which of the following is the correct way to write $$x^{\frac{3}$${4}}$$ using radicals?

Accepted Answer

$$\sqrt[4]{x^3$}$$

Question 4

Rationalize the denominator: $$\frac{5}{\sqrt{3}}.$$

Accepted Answer

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

Question 5

Simplify $$\left( 16x^8$ \$$right)^{\frac{1}$${4}}.$$

Accepted Answer

$$4x^2$$

Question 6

Which of the following is equivalent to $$\sqrt[5]{x^3$} \cdot \sqrt[5]{x^2$}$$?

Accepted Answer

$$\sqrt[5]{x^5$}$$

Question 7

If $$a \u003e 0$$ and $$b \u003e 0$$, which of the following is equivalent to $$\frac{\sqrt{a}}{\sqrt{b}}$$?

Accepted Answer

$$\sqrt{\frac{a}{b}}$$

Question 8

Simplify $$\left( x$$^{\frac{1}$${2}} y$$^{\frac{1}$${3}} \$$right)^6$$.

Accepted Answer

$$x^3$$ $$y^2$$

Question 9

Which of the following is the correct simplification of $$\sqrt[4]{81x^8$}$$?

Accepted Answer

$$3x^2$$

Question 10

A chemist needs to dilute a solution and uses the formula $$C = \sqrt{V}$$, where $$C is $$the concentration and $$V is $$the volume in liters. If the volume is increased to $$16$$ liters, what is the new concentration?

Accepted Answer

$$4$$

Question 11

Simplify the expression $$\frac{1}{\sqrt[3]{x^2$}}$$ using rational exponents.

Accepted Answer

$$x^{-2/3}$$

Question 12

Which of the following is equivalent to $$\left( 27x^6$ \$$right)^{1/3}$$?

Accepted Answer

$$3x^2$$

Question 13

Rationalize the denominator: $$\frac{7}{2\sqrt{5}}.$$

Accepted Answer

$$\frac{7\sqrt{5}}{10}$$

Question 14

Simplify $$\left( x$$^{\frac{2}$${3}} y$$^{\frac{1}$${2}} \$$right)^3$$.

Accepted Answer

$$x^2$$ $$y^{3/2}$$

Question 15

Which of the following is equivalent to $$\sqrt[6]{x^3$}$$?

Accepted Answer

$$x^{1/2}$$

Question 16

A medical researcher uses the formula $$D = \sqrt[4]{t} to $$estimate drug dosage $$D$$ based on time $$t in $$hours. If $$t = 81$$, what is the dosage?

Accepted Answer

$$3$$

Question 17

Simplify $$\sqrt{18x^4$}.$$

Accepted Answer

$$3x^2$$\sqrt{2}$$

Question 18

Which of the following is equivalent to $$\left( x$$^{1/2}$$ y$$^{1/3}$$ \$$right)^6$$?

Accepted Answer

$$x^3$$ $$y^2$$

Question 19

Simplify $$\frac{\sqrt{12}}{\sqrt{3}}.$$

Accepted Answer

$$2$$

Question 20

Which of the following is equivalent to $$x^{\frac{5}$${2}}$$?

Accepted Answer

$$\sqrt{x^5$}$$

N-th Roots and Rational Exponents: Review and Mastery

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