Question 1

Simplify the exponential expression: $$(-5x^3y$$^{-4}$$)(2x^{-1}y$$)$$. Assume that variables represent nonzero real numbers.

Accepted Answer

$$-10x^2y$$^{-3}$

Question 2

Simplify: $$\dfrac{2$$^{-8}$$x^{-1}4$$}{$$2^{-5}x$$^{-4}$$8}$$

Accepted Answer

$$x^3$$

Question 3

Simplify: $$\left(\dfrac{x^5$y^0$$}{$$x^6y$$}\$$right)^{-2}$

Accepted Answer

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

Question 4

Simplify: $$\dfrac{17.08 	imes 10$$^{-8}$$}{4 	imes 10^5$}$$ and write your answer in scientific notation.

Accepted Answer

$$4.27 	imes 10$$^{-13}$$

Question 5

Add or subtract: $$\sqrt{3x} + 7\sqrt{48x} - 3\sqrt{108x}$$

Accepted Answer

$$15\sqrt{3x}$$

Question 6

Simplify: $$y\sqrt[3]{54x} - \sqrt[3]{250xy^3$}$$

Accepted Answer

$$y\sqrt[3]{54x} - 5y\sqrt[3]{2x}$$

Question 7

Rationalize the denominator: $$\dfrac{\sqrt{6}}{\sqrt{17} + 2}$$

Accepted Answer

$$\dfrac{\sqrt{102} - 2\sqrt{6}}{13}$$

Question 8

Rationalize the denominator: $$\dfrac{2}{\sqrt{5} + \sqrt{7}}$$

Accepted Answer

$$\dfrac{2(\sqrt{5} - \sqrt{7})}{-2}$$

Question 9

Simplify using properties of exponents: $$(6x^{1/3})(3x$$^{3/2}$$)$

Accepted Answer

$$18x^{11/6}$$

Question 10

Simplify: $$\dfrac{100x$$^{2/3}$$}{10x$$^{1/4}$$}$$

Accepted Answer

$$10x^{5/12}$$

Question 11

Factor completely: $$4x^2 - 49$

Accepted Answer

$$(2x + 7)(2x - 7)$$

Question 12

Factor completely: $$27x^3 + 64$

Accepted Answer

$$(3x + 4)(9x^2$ - 12x + 16)$$

Question 13

Factor completely: $$x^2 - x - 6$

Accepted Answer

$$(x - 3)(x + 2)$$

Question 14

Simplify the rational expression and state the excluded values: $$\dfrac{3x - 2}{15x^2$ + 22x + 8}$$

Accepted Answer

$$\dfrac{3x - 2}{(3x + 4)(5x + 2)}$$, excluded: $$x = -\dfrac{4}{3}, -\dfrac{2}{5}$$

Question 15

Solve for $$x$$: $$\dfrac{x - 6}{3x} = 8 = \dfrac{x + 5}{x} ($$first, write the value(s) that make the denominator(s) zero, then solve the equation).

Accepted Answer

Excluded: $$x = 0. $$Solution: $$x = 1$$

Question 16

Solve the equation: $$\dfrac{9x}{8} - x + \dfrac{x}{40} = \dfrac{4}{5}$$

Accepted Answer

$$x = 2$$

Question 17

Solve the absolute value inequality: $$|x - 5| - 7 \leq 14$$

Accepted Answer

$$[-2, 12]$$

Question 18

Solve the linear inequality: $$-14x + 12 \u003c -2(6x - 10)$$, and express the solution in interval notation.

Accepted Answer

$$[-4, \infty)$$

Question 19

Solve the absolute value inequality: $$5 + \left|1 - \dfrac{x}{2}\right| \geq 8$$

Accepted Answer

$$(-\infty, -4] \cup [8, \infty)$$

Precalculus Review: Exponents, Radicals, Factoring, Rational Expressions, and Equations

Study Guide - Practice Questions