Question 1

Which of the following correctly simplifies $$x^3$$ \cdot $$x^5$$?

Accepted Answer

$$x^8$$

Question 2

Simplify the expression $$\left( x^2$ y^3$ \$$right)^4$$.

Accepted Answer

$$x^8$$ $$y^{12}$$

Question 3

Which property justifies the step $$\left( x^3$ y^6$ \$$right)^3$$ = x^9$ y$$^{18}$$?

Accepted Answer

Power of a Product Property

Question 4

Evaluate $$\left( -3 \$$right)^0$$.

Accepted Answer

$$1$$

Question 5

Simplify $$\dfrac{x^8$ y^5$}{x^6$ y^3$}.$$

Accepted Answer

$$x^2$$ $$y^2$$

Question 6

Which of the following is equivalent to $$\dfrac{1}{x$$^{-3}$$}$$?

Accepted Answer

$$x^3$$

Question 7

A chemist is diluting a solution and the concentration halves every hour. If the initial concentration is $$C_0$$, what is the concentration after 3 hours?

Accepted Answer

$$C_0$$ \cdot \dfrac{1}{8}$$

Question 8

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

Accepted Answer

$$4x^6$$ $$y^4$$

Question 9

Which of the following is NOT a valid application of the properties of exponents?

Accepted Answer

$$x^a + x^b = x$$^{a+b}$$

Question 10

Express $$\dfrac{3x$$^{-5}$$y^2$$}{$$6x^2y$$^{-3}$$}$$ with only positive exponents.

Accepted Answer

$$\dfrac{y^5$}{2x^7$}$$

Question 11

If $$a = 2$$ and $$b = 3$$, what is the value of $$\left( ab \$$right)^3$$?

Accepted Answer

$$216$$

Question 12

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

Accepted Answer

$$\dfrac{x$$^{12}$$}{y^8$}$$

Question 13

A biologist observes that a bacteria population triples every 2 hours. If the initial population is $$P_0$$, what is the population after 6 hours?

Accepted Answer

$$P_0$$ \cdot $$3^3$$

Question 14

Simplify $$\left( 4x^3$ y^2$ \$$right)^0$$.

Accepted Answer

$$1$$

Question 15

Which of the following is equivalent to $$\dfrac{a^5$ b$$^{-2}$$}{a$$^{-3}$$ b^4$}$$?

Accepted Answer

$$a^8$$ $$b^{-6}$$

Question 16

Simplify $$\left( 2x^2$ y$$^{-1}$$ \$$right)^3$$.

Accepted Answer

$$8x^6$$ $$y^{-3}$$

Question 17

Which of the following is undefined?

Accepted Answer

$$0^0$$

Question 18

Simplify $$\dfrac{(x^2$ y^3$)^4$$}{$$x^5$$ $$y^2$$}$.

Accepted Answer

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

Question 19

Which of the following is the correct simplification of $$\left( ab \right)^n$$?

Accepted Answer

$$a^n b^n$$

Question 20

A medication's effectiveness decreases by a factor of 4 each day. If the initial effectiveness is $$E_0$$, what is the effectiveness after 2 days?

Accepted Answer

$$E_0$$ \cdot \dfrac{1}{16}$$

Exponents: Properties, Rules, and Applications

Study Guide - Practice Questions

Study Guide - Flashcards