Question 1

Which of the following correctly applies the product rule for exponents to simplify $$x^3$$ \cdot $$x^5$$?

Accepted Answer

$$x^{8}$$

Question 2

Simplify the expression $$\dfrac{y^7$}{y^3$}$$ using the quotient rule for exponents.

Accepted Answer

$$y^{4}$$

Question 3

Which of the following is equivalent to $$a^{-4}$$?

Accepted Answer

$$\dfrac{1}{a^4$}$$

Question 4

Simplify the following expression and write your answer with positive exponents only: $$\dfrac{(x^2$y^{-3})(x$$^{-1}$$y^4$$)}{$$x^3y$$^{-2}$$}$$

Accepted Answer

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

Question 5

Which of the following is the correct simplification of $$\sqrt{50}$$ using the product rule for square roots?

Accepted Answer

$$5\sqrt{2}$$

Question 6

Rationalize the denominator and simplify: $$\dfrac{1}{\sqrt{3}}$$

Accepted Answer

$$\dfrac{\sqrt{3}}{3}$$

Question 7

Which of the following is the standard form of the polynomial $$2x^2 + 5$$ - $$3x^4 + x$?

Accepted Answer

$$-3x^4$$ + $$2x^2 + x + 5$

Question 8

What is the degree and leading coefficient of the polynomial $$f(x) = 7x^3$ - 4x^2$ + 2x - 5$$?

Accepted Answer

Degree: 3, Leading coefficient: 7

Question 9

Multiply and simplify: $$(x+2)(x+5)$$

Accepted Answer

$$x^2 + 7x + 10$

Question 10

Factor the polynomial $$x^2 - 25$ completely.

Accepted Answer

$$(x-5)(x+5)$$

Question 11

Which of the following is the correct factorization of $$6x^2 + 7x + 2$?

Accepted Answer

$$(2x+1)(3x+2)$$

Question 12

A rational expression is undefined when its denominator equals zero. For which value of $$x is$$ $$\dfrac{x+3}{x^2$-4}$$ undefined?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 13

Multiply and simplify: $$\dfrac{2x}{3} \cdot \dfrac{9}{4x}$$

Accepted Answer

$$\dfrac{3}{2}$$

Question 14

Divide and simplify: $$\dfrac{a^2$b}{4c} \div \dfrac{ab^2$}{2c^2$}$$

Accepted Answer

$$\dfrac{a c^2$}{2b}$$

Question 15

Add the rational expressions: $$\dfrac{1}{x} + \dfrac{2}{x+1}$$

Accepted Answer

Question 16

Subtract and simplify: $$\dfrac{3}{x-2} - \dfrac{1}{x-2}$$

Accepted Answer

$$\dfrac{2}{x-2}$$

Question 17

A chemist is preparing a solution and needs to simplify $$\sqrt{18} to $$measure the correct amount. What is the simplified form?

Accepted Answer

$$3\sqrt{2}$$

Question 18

A medical dosage formula involves $$\dfrac{\sqrt{27}}{3-\sqrt{2}}. $$Rationalize the denominator and simplify.

Accepted Answer

$$\dfrac{3\sqrt{3}(3+\sqrt{2})}{7}$$

Question 19

A biologist is studying population growth modeled by $$P(t) = 2$$^{3t}$$. Using exponent rules, what is P(2$$)$$?

Accepted Answer

$$2^6 = 64$

Precalculus Study Guide: Exponents, Radicals, Polynomials, and Rational Expressions

Study Guide - Practice Questions