We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Multiplying and Dividing 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 #1 : Simplifying Exponents

Simplify.

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

Possible Answers:

x^6

$x^{12}$

$x^{-12}$

$x^{-6}$

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 #331 : Exponents

Evaluate the following expression

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

Possible Answers:

$\frac{1}{2}$

$5^{20}$

$\frac{1}{25}$

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:

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

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

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

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 #1 : Simplifying Exponents

Simplify the following expression

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

Possible Answers:

6^5

6^6

36^3

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:

100,000

1,000,000

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 #2 : Simplifying Exponents

Simplify:

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

Possible Answers:

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

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

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

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

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

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 #2 : Simplifying Exponents

Simplify:

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

Possible Answers:

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

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

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

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

qrs

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

Example Question #3 : Simplifying Exponents

Simplify:

$\frac{x^{6}zy^{-9}}{x^{-4}z^2y^3}$

Possible Answers:

$\frac{x^{10}z^3}{y^6}$

$x^2z^{-1}y^6$

$\frac{y^6}{x^{10}z^3}$

$\frac{x}{yz^2}$

$\frac{x^{10}}{zy^{12}}$

Correct answer:

$\frac{x^{10}}{zy^{12}}$

Explanation:

Step 1: Use the division of exponents rule. Subtract the exponents in the numerator from the exponents in the denominator.

${x^{6+4}z^{1-2}y^{-9-3}$

$x^{10}z^{-1}y^{-12}$

Step 2: Represent the negative exponents as positive ones by moving them to the denominator:

${\color{Red} \frac{x^{10}}{zy^{12}}}$

Report an Error

View Algebra 2 Tutors

Jaahanava
Certified Tutor

University of Windsor, Master's/Graduate, Computer Science .

View Algebra 2 Tutors

Yucheng
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mechanical Engineering.

View Algebra 2 Tutors

Adeyeni
Certified Tutor

Cornell University, Bachelor in Arts, Biology (Neurobiology & Behavior).

All Algebra II Resources

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

Popular Subjects

Algebra Tutors in San Diego, English Tutors in Denver, Statistics Tutors in Denver, Statistics Tutors in Philadelphia, MCAT Tutors in Atlanta, Chemistry Tutors in New York City, GRE Tutors in Miami, Reading Tutors in Boston, Physics Tutors in Los Angeles, Computer Science Tutors in Los Angeles

Popular Courses & Classes

ISEE Courses & Classes in Atlanta, SAT Courses & Classes in Chicago, MCAT Courses & Classes in Washington DC, GRE Courses & Classes in Los Angeles, SSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Philadelphia, ACT Courses & Classes in Boston, Spanish Courses & Classes in Denver, GMAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in San Diego

Popular Test Prep

GMAT Test Prep in Houston, LSAT Test Prep in New York City, LSAT Test Prep in Boston, LSAT Test Prep in Denver, SAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Philadelphia, GRE Test Prep in Boston, ACT Test Prep in Boston, GMAT Test Prep in New York City, MCAT Test Prep in Houston

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 : Multiplying and Dividing Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Simplifying Exponents

Example Question #331 : Exponents

Example Question #2 : Simplifying Exponents

Example Question #1 : Simplifying Exponents

Example Question #4 : Simplifying Exponents

Example Question #2 : Simplifying Exponents

Example Question #2 : Simplifying Exponents

Example Question #4 : Multiplying And Dividing Exponents

Example Question #1 : Simplifying Exponents

Example Question #3 : Simplifying Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: