Question 1

Which of the following correctly applies the quotient rule for exponents to simplify $\displaystyle \frac{a^{7}}{a^{3}}$?

Accepted Answer

$a^{4}$

Question 2

A biologist is studying bacteria growth and models the population as $P = 2^{3t}$, where $t$ is time in hours. What is $P$ after 2 hours?

Accepted Answer

$2^{6}$

Question 3

Simplify the following expression using exponent rules: $(-2)^{3}(x^{4}y^{2}) \div (-8)y^{3}$

Accepted Answer

$x^{4}y^{-1}$

Question 4

Which of the following is equivalent to $\left(4x^{2}z^{3}\right)^{3}$?

Accepted Answer

$64x^{6}z^{9}$

Question 5

A chemist dilutes a solution so that its concentration is $c = 5 	imes 10^{-3}$ mol/L. What is $c$ as a fraction?

Accepted Answer

$\displaystyle \frac{5}{1000}$

Question 6

Simplify the following expression: $\displaystyle \frac{-12b^{11}}{4b^{7}}$

Accepted Answer

$-3b^{4}$

Question 7

Which of the following is the correct application of the negative exponent rule to $x^{-5}$?

Accepted Answer

$\displaystyle \frac{1}{x^{5}}$

Question 8

Simplify the following using exponent rules: $\displaystyle (3x^{4}y^{3})^{2}$

Accepted Answer

$9x^{8}y^{6}$

Question 9

A radioactive substance decays according to $A = A_{0}(\frac{1}{2})^{t}$, where $t$ is in years. If $A_{0} = 100$ grams, what is $A$ after 3 years?

Accepted Answer

$12.5$ grams

Question 10

Simplify the following expression: $\displaystyle \left(\frac{3x^{4}}{y^{-2}}\right)^{3}$

Accepted Answer

$27x^{12}y^{6}$

Question 11

Which of the following is the correct simplification of $\displaystyle (m^{-2})^{-5}$?

Accepted Answer

$m^{10}$

Question 12

A medical researcher is analyzing the growth of a virus modeled by $N = 10^{2t}$, where $t$ is in days. What is the value of $N$ after 3 days?

Accepted Answer

$10^{6}$

Question 13

Simplify the following: $\displaystyle (xy^{-3})^{2}$

Accepted Answer

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

Question 14

Which of the following is equivalent to $\displaystyle \frac{(2x^{3}y^{2})^{2}}{4x^{2}y}$?

Accepted Answer

$x^{4}y^{3}$

Question 15

Simplify the following: $\displaystyle (a^{2}b^{-3})^{4}$

Accepted Answer

$a^{8}b^{-12}$

Question 16

A physics formula involves $d = v_{0}t + \frac{1}{2}at^{2}$. If $a = 2$ and $t = 3$, what is $\frac{1}{2}at^{2}$?

Accepted Answer

$9$

Question 17

Which of the following is the correct simplification of $\displaystyle \frac{(x^{2}y^{-1})^{3}}{x^{-2}y^{2}}$?

Accepted Answer

$x^{8}y^{-5}$

Question 18

Simplify the following: $\displaystyle (2x^{-2}y^{3})^{2}$

Accepted Answer

$4x^{-4}y^{6}$

Question 19

Which of the following is the correct simplification of $\displaystyle \left(\frac{a^{3}b^{-2}}{a^{-1}b^{4}}\right)^{2}$?

Accepted Answer

$a^{8}b^{-12}$

Question 20

A population doubles every year and is modeled by $P = 100 	imes 2^{t}$. What is $P$ after 4 years?

Accepted Answer

$1600$

Exponent Rules and Simplification in College Algebra

Study Guide - Practice Questions