Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Exponents

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #801 : Mathematical Relationships And Basic Graphs

A company is constructing a wall with 4-sides, all sides are of equal length.

Write an equation using exponents to calculate the area of the wall. Use as the length and height.

Possible Answers:

$A=y\cdot y \cdot y \cdot y$

A=y^4

A=y+y

A=y^2

$A=y\cdot y$

Correct answer:

A=y^2

Explanation:

The formula to find area is:

$= length\cdot width=area$ is correct.

In our case our length is equal to our width which is .

Substituting our values into our equation we get:

$y\cdot y= A$

y^2=A

Report an Error

Example Question #1 : Simplifying Exponents

Simplify.

$x^{-6}x^3x^9$

Possible Answers:

x^6

$x^{-12}$

$x^{-6}$

$x^{12}$

Correct answer:

x^6

Explanation:

Put the negative exponent on the bottom so that you have $\frac{x^{12}}{x^{6}}$ which simplifies further to $x^{6}$ .

Report an Error

Example Question #1 : Simplifying Exponents

Evaluate the following expression

$(5^{0})^{2}$

Possible Answers:

$5^{20}$

$\frac{1}{2}$

$\frac{1}{25}$

Correct answer:

Explanation:

$(5^{0})^{2}=(1)^{2}=1$

We can also solve this problem using a different apporach

$(5^{0})^{2}=5^{0\times2}=5^{0}=1$

Remember that any number raised to the 0th power equals 1

Report an Error

Example Question #2 : Simplifying Exponents

Simplify the following expression

$((yz)^2)^{3}$

Possible Answers:

$y^{\frac{2}{3}}z^{\frac{2}{3}}$

$y^{2}z^{2}$

$y^{6}z^{6}$

Correct answer:

$y^{6}z^{6}$

Explanation:

$((yz)^{2})^{3}=(yz)^{6}=y^{6}z^{6}$

Alternatively,

$((yz)^{2})^{3}=(y^{2}z^{2})^3=y^{2\times3}z^{2\times3}=y^{6}z^{6}$

Report an Error

Example Question #3 : Simplifying Exponents

Simplify the following expression

$((6^2)^{0})^{3}$

Possible Answers:

6^5

36^3

6^6

Correct answer:

Explanation:

$((6^2)^{0})^{3}=6^{2\times 0\times 3}=6^0=1$

Remember that any number raised to the 0th power equals 1

Report an Error

Example Question #4 : Simplifying Exponents

Evaluate the following expression

$\left (\frac{10^{3}}{10^{0}} \right )^{2}$

Possible Answers:

1,000,000

100,000

Correct answer:

1,000,000

Explanation:

$\left (\frac{10^{3}}{10^{0}} \right )^{2}=\frac{10^{3\times2}}{10^{0\times2}}=\frac{10^{6}}{10^{0}}=\frac{1000000}{1}=1,000,000$

Alternatively,

$\left (\frac{10^{3}}{10^{0}} \right )^{2}=\left (10^{3-0} \right )^{2}=\left (10^{3} \right )^{2}=10^{3\times 2}=10^{6}=1,000,000$

Report an Error

Example Question #1 : Simplifying Exponents

Simplify:

$\frac{4a^{-5}b^{3}c^{2}}{12a^{-7}b^{-5}c^{-2}}$

Possible Answers:

$\frac{a^{2}b^{8}c^{4}}{3}$

$\frac{a^{-12}b^{-2}c^{0}}{3}$

$\frac{1}{3a^{-12}b^{-2}}$

$3a^{12}b^{-8}$

$\frac{4a^{2}b^{2}}{12}$

Correct answer:

$\frac{a^{2}b^{8}c^{4}}{3}$

Explanation:

$\frac{4a^{-5}b^{3}c^{2}}{12a^{-7}b^{-5}c^{-2}}$

Step 1: Simplify the exponents using the division of exponents rule (subtract exponents in demoninator from exponents in numerator).

$\frac{4a^{-5-(-7)}b^{3-(-5)}c^{2-(-2)}}{12}$

$\frac{4a^{2}b^{8}c^{4}}{12}$

Step 2: Reduce the fraction

$\frac{a^{2}b^{8}c^{4}}{3}$

Report an Error

Example Question #4 : Simplifying Exponents

Simplify:

$\frac{q^{7}r^{5}s^{16}}{q^{2}r^{3}s}$

Possible Answers:

$q^{5}r^{2}s^{15}$

$q^{3.5}r^{1.3}s^{16}$

$q^{14}r^{15}s^{16}$

qrs

$q^{9}r^{8}s^{17}$

Correct answer:

$q^{5}r^{2}s^{15}$

Explanation:

Follow the division of exponents rule. Subract the exponents in the denominator from the exponents in the numerator.

Report an Error

Example Question #4 : Multiplying And Dividing Exponents

Rewrite using a single exponent.

$\frac{(6x)^{8}}{(6x)^{3}}$

Possible Answers:

$x^{5}$

$(6x)^{24}$

$(6x)^{11}$

$x^{11}$

$(6x)^{5}$

Correct answer:

$(6x)^{5}$

Explanation:

Based on the property for dividing exponents:

$\frac{a^{m}}{a^{n}}=a^{m-n}$

In this problem, a is equal to (6x) , so

$\frac{(6x)^{8}}{(6x)^{3}}=(6x)^{8-3}=(6x)^{5}$

Report an Error

Example Question #1 : Simplifying Exponents

Simplify:

$\frac{7a^{-7}b^{-8}c^{4}}{14a^{5}b^{-9}c{}}$

Possible Answers:

$\frac{bc^3}{2a^{12}}$

$\frac{bc^3}{98a^{12}}$

$\frac{a^{12}}{2bc^3}$

$\frac{7bc^3}{14a^2}$

$\frac{2}{a^{2}bc^3}$

Correct answer:

$\frac{bc^3}{2a^{12}}$

Explanation:

Simplify:

$\frac{7a^{-7}b^{-8}c^{4}}{14a^{5}b^{-9}c{}}$

Step 1: Use the division of exponents rule, and subtract the exponents in the denominator from the exponents in the numerator

$\frac{7a^{-12}bc^3}{14}$

Step 2: Move negative exponents in the numerator to the denominator

$\frac{7bc^3}{14a^{12}}$

Step 3: Simplify

$\frac{bc^3}{2a^{12}}$

Report an Error

View Algebra 2 Tutors

John
Certified Tutor

Arizona State University, Bachelor of Science, Microbiology.

View Algebra 2 Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Algebra 2 Tutors

Irina
Certified Tutor

New York University, Bachelors, Biochemistry.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Atlanta, Physics Tutors in Chicago, Reading Tutors in New York City, Algebra Tutors in Boston, ACT Tutors in Philadelphia, GRE Tutors in Seattle, Math Tutors in Seattle, LSAT Tutors in Denver, SSAT Tutors in San Francisco-Bay Area, Calculus Tutors in Seattle

Popular Courses & Classes

Spanish Courses & Classes in Boston, Spanish Courses & Classes in Miami, SSAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in San Diego, ACT Courses & Classes in San Diego, ISEE Courses & Classes in Phoenix, LSAT Courses & Classes in Houston, LSAT Courses & Classes in Washington DC, GRE Courses & Classes in Miami

Popular Test Prep

SSAT Test Prep in Denver, SAT Test Prep in Seattle, SAT Test Prep in Washington DC, SAT Test Prep in Denver, SSAT Test Prep in Seattle, ISEE Test Prep in Phoenix, ISEE Test Prep in Denver, LSAT Test Prep in Los Angeles, SSAT Test Prep in Miami, ISEE Test Prep in Dallas Fort Worth

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #801 : Mathematical Relationships And Basic Graphs

Example Question #1 : Simplifying Exponents

Example Question #1 : Simplifying Exponents

Example Question #2 : Simplifying Exponents

Example Question #3 : Simplifying Exponents

Example Question #4 : Simplifying Exponents

Example Question #1 : Simplifying Exponents

Example Question #4 : Simplifying Exponents

Example Question #4 : Multiplying And Dividing Exponents

Example Question #1 : Simplifying Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: