Question 1

Which of the following is the correct application of the quotient property of exponents for $$\frac{x^7$}{x^3$}$$?

Accepted Answer

$$x^{4}$$

Question 2

Simplify the expression $$\$$left(2x^3$$y^2$$\$$right)^2$.

Accepted Answer

$$4x^6y^4$

Question 3

Which property justifies the step from $$a^m \cdot a^n to$$ $$a^{m+n}$$?

Accepted Answer

Product of Powers Property

Question 4

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

Accepted Answer

$$\frac{27x^6$}{y^3$}$$

Question 5

If $$x^{-2}y^3$ is rewritten with only positive exponents, what is the result?

Accepted Answer

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

Question 6

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

Accepted Answer

$$x^2$$

Question 7

Simplify $$\frac{2x$$^{-3}$$y^2$$}{$$4x^2y$$^{-1}$$}$$ and write with positive exponents.

Accepted Answer

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

Question 8

Which property is used to simplify $$\left(a^m\right)^n to$$ $$a^{mn}$$?

Accepted Answer

Power of a Power Property

Question 9

What is the simplified form of $$\left(\frac{2}{3}x$$^{-2}$$y^4$$\$$right)^{-2}$?

Accepted Answer

$$\frac{9x^4$}{4y^8$}$$

Question 10

A scientist is diluting a solution by a factor of $$10^{-3}$$ each time. After three dilutions, what is the total dilution factor?

Accepted Answer

$$10^{-9}$$

Question 11

Which of the following is the correct simplification of $$\sqrt{x^8$y^6$$}$?

Accepted Answer

$$x^4y^3$

Question 12

If $$f(x) = x^2$ - 4x + 3$$, what is $$f(2)$$?

Accepted Answer

$$-1$$

Question 13

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x+3)(x-3)$$

Question 14

Given $$g(x) = 2x^2$ - 5x + 2$$, which value of $$x is a $$root of $$g(x)$$?

Accepted Answer

$$x=2$$

Question 15

Which of the following is the correct simplification of $$\frac{a^5$b^{-2}$$}{$$a^{-3}b^4$}$$?

Accepted Answer

$$a^8b$$^{-6}$

Question 16

If $$h(x) = x^2$ + 2x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(-1, 0)$$

Question 17

Which of the following is the correct simplification of $$\left(\frac{xy^2$}{z^3$}\$$right)^2$$?

Accepted Answer

$$\frac{x^2$y^4$$}{$$z^6$$}$

Question 18

A population of bacteria triples every hour. If the initial population is $$P_0$$, what is the population after 4 hours?

Accepted Answer

$$P_0$$ \cdot $$3^4$$

Question 19

Which of the following is the correct simplification of $$\sqrt[4]{x$$^{12}$$}$$?

Accepted Answer

$$x^3$$

Question 20

If $$f(x) = 2x^2$ - 8$$, what is the $$x-$$intercept(s) of the function?

Accepted Answer

$$x = 2, x = -2$$

Properties of Square Roots and Solving Radical Equations

Study Guide - Practice Questions