Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to multiply monomial quotients

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #581 : Variables

Simplify the expression

$\frac{(3x^{4})^{2}}{2x^{3}}$ .

What is the coefficient in this expression after it is simplified?

Possible Answers:

$\frac{9}{2}$

$\frac{9}{4}$

Correct answer:

$\frac{9}{2}$

Explanation:

To simplify the expression use the rule of exponents which states that when like bases are raised to a power the exponents are multiplied together. When like bases are divided that means that their exponents are subtracted.

$\frac{(3x^{4})^{2}}{2x^{3}}$

$= \frac{3^{2}(x^{4})^{2}}{2x^{3}}$

$= \frac{9x^{4 \cdot 2}}{2x^{3}}$

$= \frac{9x^{8}}{2x^{3}}$

$= \frac{9}{2} \cdot \frac{x^{8}}{x^{3}}$

$= \frac{9}{2} \cdot x^{8-3}$

$= \frac{9}{2} x^{5}$

The coefficient of this simplified form is $\frac{9}{2}$ .

Report an Error

Example Question #582 : Variables

Simplify: $\frac{\sqrt{x} \cdot \sqrt[3]{y}}{x^2y^4}$

Possible Answers:

$x^{\frac{3}{2}} y^{\frac{11}{3}}$

$\textup{Cannot be reduced any further.}$

$x^{\frac{2}{3}} y^{\frac{3}{11}}$

$\frac{1}{x^{\frac{3}{2}} y^{\frac{11}{3}}}$

$\frac{1}{x^{\frac{2}{3}} y^{\frac{3}{11}}}$

Correct answer:

$\frac{1}{x^{\frac{3}{2}} y^{\frac{11}{3}}}$

Explanation:

In order to simplify, rewrite the numerator in terms of exponential powers.

$\frac{\sqrt{x} \cdot \sqrt[3]{y}}{x^2y^4} = \frac{x^{\frac{1}{2}} y^{\frac{1}{3}}}{x^2y^4}$

Because similar bases are divided, subtract the powers of the numerator with the denominator.

$x^{\frac{1}{2}-2}= x^{\frac{1}{2}-\frac{4}{2}} = x^{-\frac{3}{2}}$

$y^{\frac{1}{3}-4} = y^{\frac{1}{3}-\frac{12}{3}} =y^{-\frac{11}{3}}$

Since these two variables have negative exponents, we can simply take the inverse of both to eliminate the negative exponents.

$x^{-\frac{3}{2}} = \frac{1}{x^{\frac{3}{2}}}$

$y^{-\frac{11}{3}} = \frac{1}{y^{\frac{11}{3}}}$

Multiply both fractions.

The answer is: $\frac{1}{x^{\frac{3}{2}} y^{\frac{11}{3}}}$

Report an Error

View Algebra Tutors

Giles
Certified Tutor

Fourah Bay College, University of Sierra Leone, Bachelor in Arts, Physics.

View Algebra Tutors

Thuy-Thuong
Certified Tutor

Florida International University, Bachelor of Science, Health Services Administration. Florida State University, Bachelor of ...

View Algebra Tutors

Mark
Certified Tutor

University of Washington, Bachelor in Arts, Music Theory and Composition.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Phoenix, GMAT Tutors in Los Angeles, Biology Tutors in Chicago, SAT Tutors in Dallas Fort Worth, Physics Tutors in Washington DC, MCAT Tutors in San Diego, GMAT Tutors in San Francisco-Bay Area, Biology Tutors in Seattle, Chemistry Tutors in Los Angeles, ACT Tutors in Boston

Popular Courses & Classes

ACT Courses & Classes in New York City, ACT Courses & Classes in Boston, MCAT Courses & Classes in Atlanta, SAT Courses & Classes in Chicago, LSAT Courses & Classes in New York City, LSAT Courses & Classes in Phoenix, SAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Boston, GRE Courses & Classes in Washington DC, GMAT Courses & Classes in Seattle

Popular Test Prep

MCAT Test Prep in Chicago, LSAT Test Prep in Los Angeles, SSAT Test Prep in Philadelphia, SSAT Test Prep in Seattle, GMAT Test Prep in Dallas Fort Worth, LSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Atlanta, SSAT Test Prep in Boston, ACT Test Prep in Boston, LSAT Test Prep in San Diego

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 1 : How to multiply monomial quotients

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #581 : Variables

Example Question #582 : Variables

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: