Question 1

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

Accepted Answer

$$x^{8}$$

Question 2

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

Accepted Answer

$$4x^6y^4$

Question 3

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

Accepted Answer

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

Question 4

If $$a^0$$ + $$b^0 = 10$, and a$$, b 
eq 0$$, what is the value of a + b$?

Accepted Answer

Cannot be determined from the information given

Question 5

Which of the following is the correct simplification of $$\dfrac{x^7$y^3$$}{$$x^2y$$}$?

Accepted Answer

$$x^5y^2$

Question 6

A biologist is studying the growth of a bacteria population, which doubles every hour. If the initial population is $$P_0$$, which expression represents the population after $$t$$ hours?

Accepted Answer

$$P_0$$ \cdot 2^t$$

Question 7

Which of the following is the result of multiplying $$(x+2)(x-5)$$?

Accepted Answer

Question 8

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

Accepted Answer

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

Question 9

A chemist mixes two solutions, one with a concentration of $$x^2$$ and another with $$2x^2 + 3x$. What is the total concentration after mixing?

Accepted Answer

$$3x^2 + 3x$

Question 10

Which of the following is the correct expansion of $$(x+3)^2$$?

Accepted Answer

$$x^2 + 6x + 9$

Question 11

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

Accepted Answer

$$x^3$$

Question 12

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P = 5x^2$ - 20x + 15$$, where $$x is $$the number of units sold (in thousands). What is the profit if 2,000 units are sold?

Accepted Answer

$$-5$$

Question 13

Which of the following is the correct factorization of $$x^2 + 6x + 9$?

Accepted Answer

$$(x+3)^2$$

Question 14

Which of the following is the correct simplification of $$\dfrac{2x^3$y^2$$}{$$4x^2y$$}$?

Accepted Answer

$$\dfrac{1}{2}xy$$

Question 15

Which of the following is the correct expansion of $$(x-2)(x+5)$$?

Accepted Answer

$$x^2 + 3x - 10$

Question 16

Which of the following is the correct factorization of $$x^2 - 4x + 4$?

Accepted Answer

$$(x-2)^2$$

Question 17

A medical researcher models the spread of a virus with $$N = N_0$ \cdot 3^t$$, where $$N_0 is $$the initial number of cases and $$t is $$time in days. If $$N_0 = 5$ and t = 4$, what is N$?

Accepted Answer

$$405$$

Question 18

Which of the following is the correct simplification of $$\left(\dfrac{x^2$y^3$$}{$$x^5y$$}\$$right)^2$?

Accepted Answer

$$\dfrac{y^4$}{x^6$}$$

Question 19

Which of the following is the correct factorization of $$x^2 - 16$?

Accepted Answer

$$(x-4)(x+4)$$

Question 20

Which of the following is the correct simplification of $$\sqrt{50x^4$}$$?

Accepted Answer

$$5x^2$$\sqrt{2}$$

Precalculus Study Notes: Exponents and Polynomials

Study Guide - Practice Questions

Study Guide - Flashcards