We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Monomials

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

← Previous 1 2 3 4 5 6 7 8 9 10 … 15 16 Next →

Example Question #1 : How To Divide Monomial Quotients

Simplify: $\frac{5p^{7}}{25p^{^{4}}}$

Possible Answers:

$\frac{p^{-3}}{5}$

$\frac{p}{5}$

$\frac{p^{3}}{5}$

$\frac{p^{7/4}}{5}$

$5p^{3}$

Correct answer:

$\frac{p^{3}}{5}$

Explanation:

$p^{7}$ and $p^{4}$ cancel out, leaving $p^{3}$ in the numerator. 5 and 25 cancel out, leaving 5 in the denominator

Report an Error

Example Question #2 : How To Divide Monomial Quotients

Simplify the following:

$\frac{4x+6x^2}{2x}$

Possible Answers:

$\frac{2-3x}{2x}$

$\frac{1}{x}-1\frac{1}{2}$

$\frac{2}{2x}-\frac{3}{2}$

2x(2-3x)

2+3x

Correct answer:

2+3x

Explanation:

$\frac{4x+6x^2}{2x}$

First, let us factor the numerator:

4x+6x^2=x(4+6x)=2x(2+3x)

$\frac{2x(2+3x)}{2x}=2+3x$

Report an Error

Example Question #1 : How To Divide Monomial Quotients

Simplify the following:

$\frac{-2pl^2}{3yz}\div \frac{9lp^2}{5xy}$

Possible Answers:

$\frac{5}{9}$

$\frac{-18}{15xyz}$

$\frac{-18p^{3}l^{3}}{15xy^{2}z}$

$\frac{-10lx}{27zp}$

Correct answer:

$\frac{-10lx}{27zp}$

Explanation:

First, flip the numerator and the denominator of the second fraction to turn the division into multiplication.

$\frac{-2pl^2}{3yz}\div \frac{9lp^2}{5xy}=\frac{-2pl^2}{3yz} * \frac{5xy}{9lp^2}=\frac{-2pl^25xy}{3yz9lp^2}$

We can then cancel like terms.

From both the numerator and denominator, remove one , remove one , and remove one :

$\frac{-2l5x}{3z9p}$

Then we finish by multiplying the constants:

$\frac{-10lx}{27zp}$

Report an Error

Example Question #3 : How To Divide Monomial Quotients

Simplify this expression:

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

Possible Answers:

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

$\frac{z^{2}}{xy}$

$\frac{1}{xyz^{2}}$

$\frac{xy}{z^{2}}$

$xyz^{2}$

Correct answer:

$\frac{z^{2}}{xy}$

Explanation:

When different powers of the same variable are multiplied, the exponents are added. When different powers of the same variable are divided, the exponents are subtracted. So, as an example:

$\frac{x^{3}}{x} = x^{\left ( 3-1\right )} = x^{2}$

For the above problem,

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

Therefore, the expression simplifies to:

$\left ( \frac{1}{x} \right ) \left ( \frac{1}{y} \right ) z^{2} = \frac{z^{2}}{xy}$

Report an Error

Example Question #11 : Multiplying And Dividing Exponents

Simplify the rational expression.

$\frac{12x^2y^4z^6}{6xz^{12}}$

Possible Answers:

$\frac{2xy^4}{z^6}$

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

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

$\frac{2xy^4}{z^2}$

Correct answer:

$\frac{2xy^4}{z^6}$

Explanation:

$\frac{12x^2y^4z^6}{6xz^{12}}$

To simplify variables with exponents through division, you must subtract the exponent in the denominator from the numerator.

$\frac{12}{6}(x^{2-1})(y^{4-0})(z^{6-12})=2xy^4z^{-6}=\frac{2xy^4}{z^6}$

Remember that negative exponents will eventually be moved back to the denominator.

Report an Error

Example Question #31 : Simplifying Expressions

Divide the fractions.

$\frac{30xy}{11} \div \frac{25x^{3}}{22y}$

Possible Answers:

$\frac{5x^{4}}{12}$

$\frac{5x^{2}}{12y^{2}}$

$\frac{5y^{2}}{12x^{2}}$

$\frac{12y^{2}}{5x^{2}}$

$\frac{12x^{4}}{5}$

Correct answer:

$\frac{12y^{2}}{5x^{2}}$

Explanation:

$\frac{30xy}{11} \div \frac{25x^{3}}{22y}$

Dividing fractions is equal to multiplying by the reciprocal.

$\frac{30xy}{11} * \frac{22y}{25x^{3}}$

Cross-cancel the 30 with the 25, and the 22 with the 11.

$\frac{6xy}{1} *\frac{2y}{5x^{3}}$

Combine via multiplication and simplify.

$\frac{6xy* 2y}{5x^{3}}=\frac{6* 2*x* y*y}{5x^{3}}=\frac{12y^{2}}{5x^{2}}$

Report an Error

Example Question #12 : Multiplying And Dividing Exponents

Simplify $\frac{a^{4}b^{2}}{6a^{3}b}\div \frac{2b^{5}}{12a^{7}}$

Possible Answers:

$\frac{b^4}{a^8}$

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

$\frac{b^6}{36a^6}$

$\frac{a^8}{b^4}$

Correct answer:

$\frac{a^8}{b^4}$

Explanation:

Rewrite so that you are multiplying the reciprocal of the second fraction:

$\frac{a^{4}b^{2}}{6a^{3}b}\times \frac{12a^{7}}{2b^{5}}$

You can then simplify using rules of exponents:

$\frac{12a^{11}b^2}{12a^3b^6}=\frac{a^8}{b^4}$

Report an Error

Example Question #51 : Monomials

Evaluate: $3x^3 \div 6x$

Possible Answers:

2x^2

$\frac{1}{2}x^2$

$\frac{1}{2}x$

Correct answer:

$\frac{1}{2}x^2$

Explanation:

First, divide the coefficients.

$3\div 6 = \frac{1}{2}$ .

Now consider the variables. x^3 means x times itself 3 times. Doing $x^3 \div x$ is the same as $\frac{x*x*x}{x}$ .

We see that an x from the top can cancel with the x on the bottom, leaving $\frac{x*x}{1}$ , or x^2 . Our answer then is $\frac{1}{2}x^2$ .

Report an Error

Example Question #11 : How To Divide Monomial Quotients

Divide: $\frac{x^2}{x^{-1}}$

Possible Answers:

x^3

$\frac{1}{x^3}$

$\frac{1}{x}$

-x^3

Correct answer:

x^3

Explanation:

Dividing exponents by the same base allows the powers to be subtracted. Rewrite the exponents as one base.

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

Report an Error

Example Question #53 : Monomials

Find the result of

$\frac{12x^3\cdot2x^4}{3x^5}$ .

Possible Answers:

$8x^{7/5}$

12x^3

8x^2

$24x^{12}$

Correct answer:

8x^2

Explanation:

The question asks for the quotient of $\frac{12x^3\cdot2x^4}{3x^5}$ .

We can rewrite the expression using the rules of multiplication and exponents to find the answer of 8x^2 .

$\frac{12\cdot2\cdot x\cdotx^{3+4}}{3x^5}= \frac{24}{3}\cdot x^{3+4-5}= 8x^2$

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 … 15 16 Next →

View Algebra Tutors

Swagatika
Certified Tutor

Regional Institute of Education Bhubaneswar, Bachelor of Economics, Mathematics.

View Algebra Tutors

Ayan
Certified Tutor

Vellore Institute of Technology, Bachelor, Chemical Engineering. University of Calgary, Master's/Graduate, Chemical and Petro...

View Algebra Tutors

Rima
Certified Tutor

Lebanese university , Master's/Graduate, Marketing and Management .

All Algebra 1 Resources

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

Popular Subjects

Calculus Tutors in Dallas Fort Worth, Math Tutors in Boston, LSAT Tutors in Philadelphia, English Tutors in Chicago, ISEE Tutors in Philadelphia, SAT Tutors in Seattle, Chemistry Tutors in Houston, SSAT Tutors in Los Angeles, ACT Tutors in Chicago, Physics Tutors in Seattle

Popular Courses & Classes

ACT Courses & Classes in Phoenix, GRE Courses & Classes in Seattle, SAT Courses & Classes in Denver, Spanish Courses & Classes in Houston, LSAT Courses & Classes in Seattle, SSAT Courses & Classes in Phoenix, GRE Courses & Classes in Houston, SAT Courses & Classes in New York City, LSAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Seattle

Popular Test Prep

SAT Test Prep in Phoenix, LSAT Test Prep in Houston, ISEE Test Prep in Los Angeles, SAT Test Prep in New York City, SSAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Los Angeles, SAT Test Prep in Miami, GMAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Atlanta, GRE 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 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Divide Monomial Quotients

Example Question #2 : How To Divide Monomial Quotients

Example Question #1 : How To Divide Monomial Quotients

Example Question #3 : How To Divide Monomial Quotients

Example Question #11 : Multiplying And Dividing Exponents

Example Question #31 : Simplifying Expressions

Example Question #12 : Multiplying And Dividing Exponents

Example Question #51 : Monomials

Example Question #11 : How To Divide Monomial Quotients

Example Question #53 : Monomials

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: