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 #1 : How To Multiply Monomial Quotients

Simplify:

$\frac{a^{2}b}{c^{4}}*\frac{c^{6}}{a^{5}b^{6}}$

Possible Answers:

$\frac{1}{a^{7}b^{7}c^{10}}$

$3a^{7}b^{7}c^{10}$

$\frac{a^{3}b^{5}}{c^{2}}$

$a^{\frac{2}{5}}b^{\frac{1}{7}}c^{\frac{3}{2}}$

$\frac{c^{2}}{a^{3}b^{5}}$

Correct answer:

$\frac{c^{2}}{a^{3}b^{5}}$

Explanation:

Since there are no like terms in the numerator or in the denominator, you can only combine ther terms on the numerator and denominator so that they are in one quotient.

$\frac{a^{2}b}{c^{4}}*\frac{c^{6}}{a^{5}b^{6}}=\frac{a^{2}bc^{6}}{a^{5}b^{6}c^{4}}$

Use the rules of exponents $\frac{x^{a}}{x^{b}}=x^{a-b}$ and $x^{-a}=\frac{1}{x^{a}}$ to further simplify the expression by combining the terms $a^{2}$ and $a^{5}$ , and $b^{6}$ , and $c^{6}$ and $c^{4}$ .

$\frac{a^{2}bc^{6}}{a^{5}b^{6}c^{4}}=a^{-3}b^{-5}c^{2}=\frac{c^{2}}{a^{3}b^{5}}$

Report an Error

Example Question #531 : Variables

Simplify:

$\frac{x^{2}y^{2}}{4z}*\frac{16x^{4}yz^{2}}{y^{3}}$

Possible Answers:

$4x^{6}yz$

$4x^{6}y^{0}z^{2}$

$\frac{4x^{6}}{y^{6}z^{3}}$

$4x^{6}z$

$4x^{6}y^{6}z^{3}$

Correct answer:

$4x^{6}z$

Explanation:

Divide both integers by the GCF (4).

$\frac{x^{2}y^{2}}{4z}*\frac{16x^{4}yz^{2}}{y^{3}}=\frac{x^{2}y^{2}}{z}*\frac{4x^{4}yz^{2}}{y^{3}}$

Organize the variables so like terms are together in the numerator and in the denominator. Then use rules of exponents to combine $x^{2}$ and $x^{4}$ and $y^{2}$ and in the numerator. Remember the following exponent rule: $x^{a}*x^{b}=x^{a+b}$ ,

$\frac{x^{2}y^{2}}{z}*\frac{4x^{4}yz^{2}}{y^{3}}=\frac{4x^{2}x^{4}y^{2}yz^{2}}{y^{3}z}=\frac{4x^{6}y^{3}z^{2}}{y^{3}z}$

Since $y^{3}$ is in the numerator and the denominator, you can cancel it out.

$\frac{4x^{6}y^{3}z^{2}}{y^{3}z}=\frac{4x^{6}z^{2}}{z}$

Use the exponent rule $\frac{x^{a}}{x^{b}}=x^{a-b}$ to further simplify the expression by combining the terms $z^{2}$ and .

$\frac{4x^{6}z^{2}}{z}=4x^{6}z$

Report an Error

Example Question #532 : Variables

Simplify:

$\frac{3a^{2}}{b^{4}}*\frac{4b}{a}*\frac{a^{2}b^{4}}{2}$

Possible Answers:

$6a^{4}b^{\frac{5}4{}}$

$\frac{6}{a^{5}b^{9}}$

$6a^{5}b^{9}$

$\frac{6}{a^{3}b}$

$6a^{3}b$

Correct answer:

$6a^{3}b$

Explanation:

Divide both 4 and 2 by the GCF (2) and organize the variables so like terms are together in the numerator and in the denominator. Multiply the integers 4 and 3 together.

$\frac{3a^{2}}{b^{4}}*\frac{4b}{a}*\frac{a^{2}b^{4}}{2}=\frac{3a^{2}}{b^{4}}*\frac{2b}{a}*\frac{a^{2}b^{4}}{1}=\frac{2*3*a^{2}a^{2}bb^{4}}{ab^{4}}=\frac{6a^{2}a^{2}bb^{4}}{ab^{4}}$

Then use rules of exponents to combine $a^{2}$ and $a^{2}$ and and $b^{4}$ in the numerator. Remember the following exponent rule: $x^{a}*x^{b}=x^{a+b}$ ,

$\frac{6a^{2}a^{2}bb^{4}}{ab^{4}}=\frac{6a^{4}b^{5}}{ab^{4}}$

Use the exponent rule $\frac{x^{a}}{x^{b}}=x^{a-b}$ to further simplify the expression by combining the terms $a^{4}$ and and $b^{5}$ and .

$\frac{6a^{4}b^{5}}{ab^{4}}=6a^{3}b$

Report an Error

Example Question #533 : Variables

Simplify:

$\frac{12x^{3}y^{5}z^{12}}{3}*\frac{6xyz}{30x^{4}y^{3}z^{2}}$

Possible Answers:

$\small \frac{4y^{3}z^{11}}{5}$

$\small \frac{5x^{8}y^{9}z^{15}}{4}$

$\small \frac{5}{4y^{3}z^{11}}$

$\small \frac{4}{5x^{8}y^{9}z^{15}}$

$\small \frac{4}{5y^{9}z^{15}}$

Correct answer:

$\small \frac{4y^{3}z^{11}}{5}$

Explanation:

In the first quotient, divide 12 and 3 by the GCF (3). In the second quotient, divide 6 and 30 by the GCF (6). You could also divide all the intergers by 2, but it would take longer to simplify since you would end up with larger numbers.

$\frac{12x^{3}y^{5}z^{12}}{3}*\frac{6xyz}{30x^{4}y^{3}z^{2}}=4x^{3}y^{5}z^{12}*\frac{xyz}{5x^{4}y^{3}z^{2}}$

Organize the variables so like terms are together in the numerator and in the denominator. Then use rules of exponents to combine $x^{3}$ and and $y^{5}$ and and $z^{12}$ and in the numerator. Remember the following exponent rule: $x^{a}*x^{b}=x^{a+b}$ ,

$\small 4x^{3}y^{5}z^{12}*\frac{xyz}{5x^{4}y^{3}z^{2}}=\frac{4x^{3}xy^{5}yz^{12}z}{5x^{4}y^{3}z^{2}}=\frac{4x^{4}y^{6}z^{13}}{5x^{4}y^{3}z^{2}}$

Since $x^{4}$ is in the numerator and the denominator, you can cancel it out.

$\small \frac{4x^{4}y^{6}z^{13}}{5x^{4}y^{3}z^{2}}=\frac{4y^{6}z^{13}}{5y^{3}z^{2}}$

Use the exponent rule $\frac{x^{a}}{x^{b}}=x^{a-b}$ to further simplify the expression by combining the terms $y^{6}$ and $y^{3}$ and $z^{13}$ and $\small z^{2}$ .

$\small \frac{4y^{6}z^{13}}{5y^{3}z^{2}}=\frac{4y^{3}z^{11}}{5}$

Report an Error

Example Question #2 : How To Multiply Monomial Quotients

Simplify:

$\frac{a^{2}b^{4}}{4a^{5}}*\frac{2by^{4}}{y^{3}}$

Possible Answers:

$\frac{2b^{5}y}{4a^{3}}$

$\frac{2a^{3}}{yb^{5}}$

$\frac{yb^{5}}{2a^{3}}$

$\frac{a^{\frac{2}{5}}b^{5}}{2y^{\frac{4}{3}}}$

$\frac{2a^{2}b^{5}y^{4}}{4a^{5}y^{3}}$

Correct answer:

$\frac{yb^{5}}{2a^{3}}$

Explanation:

First, organize the variables so like terms are together in the numerator and in the denominator.

$\frac{2a^{2}b^{4}by^{4}}{4a^{5}y^{3}}$

Second, use rules of exponents to combine the following terms: $b^{4}$ and , $a^{2}$ and $a^{5}$ , and $y^{4}$ and $y^{3}$ . Remember the following exponent rules:

$x^{a}*x^{b}=x^{a+b}$

$\frac{x^{a}}{x^{b}}=x^{a-b}$

$x^{-a}=\frac{1}{x^{a}}$

$\frac{2a^{2}b^{4}by^{4}}{4a^{5}y^{3}}=\frac{2a^{-3}b^{5}y}{4}=\frac{2b^{5}y}{4a^{3}}$

Third, divide the 2 and the 4 by the GCF, 2.

$\frac{2a^{2}b^{4}by^{4}}{4a^{5}y^{3}}=\frac{2b^{5}y}{4a^{3}}=\frac{yb^{5}}{2a^{3}}$

Report an Error

Example Question #3 : How To Multiply Monomial Quotients

Simplify:

$\frac{24x^{5}}{6y^{2}}*\frac{14y^{4}x}{21}$

Possible Answers:

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

$\frac{8y^{-2}}{3x^{5}}$

$\frac{8y^{2}x^{6}}{3}$

$\frac{8y^{4}x^{6}}{3y^{2}}$

$\frac{3}{8y^{2}x^{6}}$

Correct answer:

$\frac{8y^{2}x^{6}}{3}$

Explanation:

Divide 6 and 24 by 6 (the GCF) and 14 and 21 by 7 (the GCF). Combine like terms in the numerator and the denominator.

$\frac{24x^{5}}{6y^{2}}*\frac{14y^{4}x}{21}=\frac{4x^{5}}{y^{2}}*\frac{2y^{4}x}{3}=\frac{4*2*y^{4}x^{5}x}{3y^{2}}=\frac{8y^{4}x^{5}x}{3y^{2}}$

Use rules of exponents to combine the following terms: $y^{4}$ and $y^{2}$ and $x^{5}$ and Remember the following exponent rules:

$x^{a}*x^{b}=x^{a+b}$

and

$\frac{x^{a}}{x^{b}}=x^{a-b}$

$\frac{8y^{4}x^{5}x}{3y^{2}}=\frac{8y^{4}x^{6}}{3y^{2}}=\frac{8y^{2}x^{6}}{3}$

Report an Error

Example Question #1 : How To Multiply Monomial Quotients

Simplify:

$\frac{10x^{3}}{b^{6}}*\frac{2b^{2}}{5x^{3}}$

Possible Answers:

$\frac{4x^{3}b^{2}}{x^{3}b^{6}}$

$\frac{20x^{3}b^{2}}{5x^{3}b^{6}}$

$\frac{b^{4}}{4}$

$\frac{4x^{3}}{x^{3}b^{4}}$

$\frac{4}{b^{4}}$

Correct answer:

$\frac{4}{b^{4}}$

Explanation:

Combine like terms in the numerator and the denominator. Then, divide 20 and 5 by 5 (the GCF).

$\frac{10 * 2*x^{3}b^{2}}{5x^{3}b^{6}}=\frac{20x^{3}b^{2}}{5x^{3}b^{6}}=\frac{4x^{3}b^{2}}{x^{3}b^{6}}$

The GCF rule can also be used to remove $x^{3}$ from the numerator and the deonominator. $x^{3}$ goes into $x^{3}$ once.

$\frac{4x^{3}b^{2}}{x^{3}b^{6}}=\frac{4b^{2}}{b^{6}}$

Use rules of exponents to combine the terms $b^{2}$ and $b^{6}$ . Remember the following exponent rules:

$\frac{x^{a}}{x^{b}}=x^{a-b}$

$x^{-a}=\frac{1}{x^{a}}$

$\frac{4b^{2}}{b^{6}}=4b^{-4}=\frac{4}{b^{4}}$

Report an Error

Example Question #4 : How To Multiply Monomial Quotients

Simplify:

$\frac{6x^{2}y^{2}z}{8z^{4}}*\frac{4xy^{3}}{20y}$

Possible Answers:

$\frac{3x^{3}y^{4}z^{5}}{20}$

$\small \frac{3x^{3}y^{4}}{20z^{3}}$

$\frac{3}{20}x^{3}y^{4}z^{4}$

$\frac{3x^{3}y^{6}z^{5}}{20}$

$\frac{3x^{3}y^{\frac{5}{1}}z^{\frac{1}{4}}}{20}$

Correct answer:

$\small \frac{3x^{3}y^{4}}{20z^{3}}$

Explanation:

In the first quotient, divide 6 and 8 by the GCF (2). In the second quotient, divide 4 and 20 by the GCF (4).

$\frac{6x^{2}y^{2}z}{8z^{4}}*\frac{4xy^{3}}{20y}=\frac{3x^{2}y^{2}z}{4z^{4}}*\frac{xy^{3}}{5y}$

Organize the variables so like terms are together in the numerator and in the denominator. Then use rules of exponents to combine $x^{2}$ and and $y^{2}$ and $y^{3}$ in the numerator. Remember the following exponent rule:

$x^{a}*x^{b}=x^{a+b}$

$\small \small \frac{3x^{2}y^{2}z}{4z^{4}}*\frac{xy^{3}}{5y}=\frac{3x^{2}xy^{2}y^{3}z}{20yz^{4}}=\frac{3x^{3}y^{5}z}{20yz^{4}}$

Use the rules of exponents

$\frac{x^{a}}{x^{b}}=x^{a-b}$

and

$x^{-a}=\frac{1}{x^{a}}$

to further simplify the expression by combining the terms $\small y^{5}$ and $\small y$ , and $\small z$ and $\small z^{4}$ .

$\small \frac{3x^{3}y^{5}z}{20yz^{4}}=\frac{3x^{3}y^{4}z^{-3}}{20}=\frac{3x^{3}y^{4}}{20z^{3}}$

Report an Error

Example Question #535 : Variables

Simplify:

$\frac{27a^{3}bc}{9a^{5}b^{7}}*\frac{20b^{4}c^{2}}{16a}$

Possible Answers:

$\frac{15}{4a^{3}b^{2}c^{3}}$

$\frac{15a^{\frac{1}{2}}b^{\frac{5}{7}}c^{3}}{4}$

$\frac{15a^{3}b^{2}c^{3}}{4}$

$\frac{4a^{3}b^{2}}{15c^{3}}$

$\frac{15c^{3}}{4a^{3}b^{2}}$

Correct answer:

$\frac{15c^{3}}{4a^{3}b^{2}}$

Explanation:

First, in the first quotient, divide 27 and 9 by the GCF (9). In the second quotient, divide 20 and 16 by the GCF (4).

$\frac{27a^{3}bc}{9a^{5}b^{7}}*\frac{20b^{4}c^{2}}{16a}=\frac{3a^{3}bc}{a^{5}b^{7}}*\frac{5b^{4}c^{2}}{4a}$

Second, organize the variables so like terms are together in the numerator and in the denominator.

$\frac{3a^{3}bc}{a^{5}b^{7}}*\frac{5b^{4}c^{2}}{4a}=\frac{3*5*a^{3}bb^{4}cc^{2}}{4a^{5}ab^{7}}$

Third, multiply the integers and use the rules of exponents to combine the following terms: $a^{5}$ and , and $b^{4}$ , and and $c^{2}$ . Remember the following exponent rule: $x^{a}*x^{b}=x^{a+b}$ ,

$\frac{3*5*a^{3}bb^{4}cc^{2}}{4a^{5}ab^{7}}=\frac{15a^{3}b^{5}c^{3}}{4a^{6}b^{7}}$

Fourth, use the rules of exponents

$\frac{x^{a}}{x^{b}}=x^{a-b}$

and

$x^{-a}=\frac{1}{x^{a}}$

to further simplify the expression by combining the terms $a^{3}$ and $a^{6}$ and $b^{5}$ and $b^{7}$ .

$\frac{15a^{3}b^{5}c^{3}}{4a^{6}b^{7}}=\frac{15a^{-3}b^{-2}c^{2}}{4}=\frac{15c^{3}}{4a^{3}b^{2}}$

Report an Error

Example Question #4771 : Algebra 1

Simplify:

$\frac{a^{7}b^{6}c^{4}}{8}*\frac{28b^{3}}{12a^{3}b^{2}}$

Possible Answers:

$\frac{7c^{4}}{6a^{10}b^{11}}$

$\frac{7a^{4}b^{7}c^{4}}{6}$

$\frac{7a^{4}b^{7}c^{4}}{24}$

$\frac{24}{7a^{4}b^{7}c^{4}}$

$\frac{7a^{\frac{7}{3}}b^{\frac{9}{2}}c^{4}}{24}$

Correct answer:

$\frac{7a^{4}b^{7}c^{4}}{24}$

Explanation:

Because 28 and 12, the coefficients in the second quotient, share common factors, you can divide them by the GCF (4). Because the cofficients in the first quotient are technically 1 and 8, you cannot further reduce the 8.

$\frac{a^{7}b^{6}c^{4}}{8}*\frac{28b^{3}}{12a^{3}b^{2}}=\frac{a^{7}b^{6}c^{4}}{8}*\frac{7b^{3}}{3a^{3}b^{2}}$

Organize the variables so like terms are together in the numerator and in the denominator. Then, multiply and in the denominator and use rules of exponents to combine $b^{6}$ and $b^{3}$ in the numerator. Remember the following exponent rule: $x^{a}*x^{b}=x^{a+b}$ ,

$\frac{7a^{7}b^{6}b^{3}c^{4}}{8*3a^{3}b^{2}}=\frac{7a^{7}b^{6}b^{3}c^{4}}{24a^{3}b^{2}}=\frac{7a^{7}b^{9}c^{4}}{24a^{3}b^{2}}$

Use the exponent rule

$\frac{x^{a}}{x^{b}}=x^{a-b}$

to further simplify the expression by combining the terms $a^{7}$ and $a^{3}$ and $b^{9}$ and $b^{2}$ .

$\frac{7a^{7}b^{9}c^{4}}{24a^{3}b^{2}}=\frac{7a^{4}b^{7}c^{4}}{24}$

Report an Error

View Algebra Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

View Algebra Tutors

Nate
Certified Tutor

University of Wisconsin-Oshkosh, non degree, Prepharmacy. University of Wisconsin-Madison, Pharmaceutical Chemist, Pharmacy.

View Algebra Tutors

Sumaiya
Certified Tutor

CUNY Brooklyn College, Bachelors, Business for Health Professions. CUNY Brooklyn College, Masters, Masters in Business.

All Algebra 1 Resources

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

Popular Subjects

GMAT Tutors in Chicago, Reading Tutors in Boston, GMAT Tutors in Denver, ISEE Tutors in San Francisco-Bay Area, Algebra Tutors in Houston, Chemistry Tutors in Phoenix, Chemistry Tutors in Miami, French Tutors in Atlanta, Calculus Tutors in New York City, Math Tutors in Dallas Fort Worth

Popular Courses & Classes

Spanish Courses & Classes in Boston, MCAT Courses & Classes in Miami, GMAT Courses & Classes in Boston, GMAT Courses & Classes in Los Angeles, ACT Courses & Classes in Denver, GRE Courses & Classes in Chicago, MCAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Seattle, GMAT Courses & Classes in Houston

Popular Test Prep

MCAT Test Prep in Philadelphia, SSAT Test Prep in Houston, GMAT Test Prep in Chicago, LSAT Test Prep in San Diego, MCAT Test Prep in Boston, ISEE Test Prep in New York City, GMAT Test Prep in Los Angeles, ISEE Test Prep in Atlanta, ACT Test Prep in San Diego, LSAT Test Prep in Miami

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 #1 : How To Multiply Monomial Quotients

Example Question #531 : Variables

Example Question #532 : Variables

Example Question #533 : Variables

Example Question #2 : How To Multiply Monomial Quotients

Example Question #3 : How To Multiply Monomial Quotients

Example Question #1 : How To Multiply Monomial Quotients

Example Question #4 : How To Multiply Monomial Quotients

Example Question #535 : Variables

Example Question #4771 : Algebra 1

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: