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 expression $$\dfrac{2$$^{-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

$$16\sqrt{3x}$$

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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 values: $$x = -\dfrac{4}{3}, -\dfrac{2}{5}$$

Question 11

Solve for $$x$$: $$\dfrac{x - 6}{3x} = \dfrac{x + 5}{x} - 8$$ and state the value(s) that make the denominator zero.

Accepted Answer

Denominator zero at $$x = 0$$; solution $$x = -3$$

Question 12

Solve the equation using the quadratic formula: $$x^2 + 5x = 2$.

Accepted Answer

$$x = \dfrac{-5 \pm \sqrt{33}}{2}$$

Question 13

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

Accepted Answer

$$[-2, 12]$$

Question 14

Given the formula $$N = 4x^2$ + 5x + 3$$ for the number of households $$N (in $$thousands) with computers $$x$$ years after 1990, in what year were there 87 thousand households with computers?

Accepted Answer

1994

Question 15

Solve the radical equation and check all proposed solutions: $$3\sqrt{x + 8} = x + 4.$$

Accepted Answer

$$x = 8$$

Question 16

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

Accepted Answer

$$[-4, \infty)$$

Question 17

Solve the absolute value inequality: $$5 + |1 - \dfrac{x}{2}| \geq 8$$ and express the solution in interval notation.

Accepted Answer

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

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

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