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

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