$$\frac{3x - 2}{(3x + 4)(5x + 2)}$$, $$x \neq -\frac{4}{3}, -\frac{2}{5}$$

Question 1

Simplify the expression $$(-5x^3y$$^{-4}$$)(2x^{-1}y$$)$$, assuming all variables represent nonzero real numbers.

Accepted Answer

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

Question 2

Simplify the exponential expression: $$2^{-8}x$$^{-1}$$4$.

Accepted Answer

$$2^{-6}x$$^{-1}$

Question 3

Simplify the expression: $$\left(\frac{x^5$y}{x^6$y}\$$right)^{-2}$$.

Accepted Answer

Question 4

Evaluate $$\frac{17.08 	imes 10$$^{-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: $$\frac{\sqrt{6}}{\sqrt{17} + 2}.$$

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

$$\frac{3x - 2}{(3x + 4)(5x + 2)}$$, $$x 
eq -\frac{4}{3}, -\frac{2}{5}$$

Question 13

Perform the indicated operation: $$\frac{3}{x} + \frac{7}{x-4}.$$

Accepted Answer

$$\frac{3(x-4) + 7x}{x(x-4)}$$

Question 14

Solve for $$x$$: $$\frac{x-6}{3x} = \frac{x+5}{x} - 8.$$

Accepted Answer

$$x = -3$$

Question 15

Solve the equation: $$9x/8 - x + x/40 = 4/5.$$

Accepted Answer

$$x = 2$$

Question 16

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

Accepted Answer

$$[-2, 21]$$

Question 17

Solve the linear inequality: $$-14x + 12 \u003c -2(6x - 10).$$

Accepted Answer

$$[-4, \infty)$$

Question 18

Solve the absolute value inequality: $$5 + |1 - \frac{x}{2}| \geq 8.$$

Accepted Answer

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

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

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