Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Middle Level Math : Operations

Study concepts, example questions & explanations for ISEE Middle Level Math

Create An Account

All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : How To Multiply Variables

Simplify:

$(2)(15y^{2})(x^{3})(10)$

Possible Answers:

$300x^{3}y^{2}$

$27 x^{4}y^{2}$

$27x^{3}y^{2}$

$30x^{31}y^{2}$

$20x^{4}y^{30}$

Correct answer:

$300x^{3}y^{2}$

Explanation:

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

$(2 * 15 * 10)(x^{3})(y^{2})$

There are no variables to combine. We only need to combine the numerical coefficient. This gets you:

$(300)(x^{3})(y^{2})$

This is the same as:

$300x^{3}y^{2}$

Report an Error

Example Question #671 : Concepts

Simplify:

$x * y * (x^{3}) * (xy)$

Possible Answers:

$6x^{3}y$

$3x^{5}y^{2}$

10xy

$x^{3}y$

$x^{5}y^{2}$

Correct answer:

$x^{5}y^{2}$

Explanation:

$(x * x* x^{3})(y * y)$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(x^{1+1+3})(y^{1+1})$

$(x^{5})(y^{2})$

This is the same as:

$x^{5}y^{2}$

Report an Error

Example Question #1267 : Hspt Mathematics

Simplify:

$x * a^{3} * y^{4} * x^{2} * x*a^{2}$

Possible Answers:

$a^{6}xy^{2}$

$a^{6}x^{2}y^{4}$

80axy

$a^{5}x^{3}y^{4}$

$a^{5}x^{4} y^{4}$

Correct answer:

$a^{5}x^{4} y^{4}$

Explanation:

$(a^{3} * a^{2})(x * x^{2} * x)(y^{4})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(a^{3+2})(x^{1+2+1})(y^4)$

$(a^{5})(x^{4})(y^{4})$

This is the same as:

$a^{5}x^{4} y^{4}$

Report an Error

Example Question #32 : How To Multiply Variables

Simplify:

$xy(x^{2} + 2aby)$

Possible Answers:

$3abx^{3}y^{2}$

$x^{2}y + 2abxy$

$3abx^{3}y$

$2x^{2}y + 4abxy$

$x^{3}y + 2abxy^{2}$

Correct answer:

$x^{3}y + 2abxy^{2}$

Explanation:

$xy(x^{2} + 2aby)$

Distribute the outside term into the parentheses. Multiply each term in parentheses by :

$(xy)(x^{2}) + (xy)(2aby)$

Now, for each member, move the similar variables into separate groups. You can do this because of the associative rule for multiplication:

$(x*x^{2})(y) + (2)(a)(b)(x)(y*y)$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(x^{1+2})(y)+(2)(a)(b)(x)(y^{1+1})$

$(x^{3})(y) + (2)(a)(b)(x)(y^2)$

This is the same as:

$x^{3}y + 2abxy^{2}$

Report an Error

Example Question #31 : Operations

Simplify:

2ab(5xy - 3ax + 4by)

Possible Answers:

$12a^{4}b^{4}x^{2}y^{2}$

$7abxy – 5a^{2}bx + 6ab^{2}y$

$10abxy - 6a^{2}bx + 8ab^{2}y$

12abxy

6abxy - 6abx + 5aby

Correct answer:

$10abxy - 6a^{2}bx + 8ab^{2}y$

Explanation:

2ab(5xy - 3ax + 4by)

Distribute the outside term into the parentheses. Multiply each term in parentheses by 2ab :

(2ab)(5xy) - (2ab)(3ax)+ (2ab)(4by)

Now, for each member, move the similar variables into separate groups. You can do this because of the associative rule for multiplication:

(2*5)(abxy) - (2*3)(a*a)(bx)+ (2*4)(a)(b*b)(y)

When multiplying variables of the same type, you add their exponents together. This gets you:

$(10)(abxy)-(6)(a^{1+1})(bx)+(8)(a)(b^{1+1})(y)$

$(10)(abxy) - (6)(a^{2})(bx)+ (2*4)(a)(b^{2})(y)$

This is the same as:

$10abxy - 6a^{2}bx + 8ab^{2}y$

Report an Error

Example Question #32 : Operations

Simplify:

$5bv(vx^{2} - 10bx - 5vb^{6})$

Possible Answers:

$5bv^{2}x^{2} + 50b^{2}v^{2}x – 25b^{7}$

$6bv^{2}x^{2} – 5b^{2}v^{2}x$

$10bv^{2}x^{2} – 50bv^{2}x – 10b^{5}v^{2}$

$5bv^{2}x^{2} - 50b^{2}vx - 25b^{7}v^{2}$

Correct answer:

$5bv^{2}x^{2} - 50b^{2}vx - 25b^{7}v^{2}$

Explanation:

$5bv(vx^{2} - 10bx - 5vb^{6})$

Distribute the outside term into the parentheses. Multiply each term in parentheses by 5bv :

$(5bv)(vx^{2}) - (5bv)(10bx) - (5bv)(5vb^{6})$

Now, for each member, move the similar variables into separate groups. You can do this because of the associative rule for multiplication:

$(5)(b)(v * v)(x^{2}) - (5 * 10)(b *b)(vx) - (5*5)(b *b^{6})(v*v)$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(5)(b)(v^{1+1})(x^2)-(50)(b^{1+1})(vx)-(25)(b^{1+6})(v^{1+1})$

$(5)(b)(v^{2})(x^{2}) - (50)(b^{2})(vx) - (25)(b^{7})(v^{2})$

This is the same as:

$5bv^{2}x^{2} - 50b^{2}vx - 25b^{7}v^{2}$

Report an Error

Example Question #61 : Algebra

$x^{2}* x^{5}=$

Possible Answers:

$x^{7}$

$x^{3}$

Cannot be simplified further

Correct answer:

$x^{7}$

Explanation:

To simplify, add the exponents:

$x^{2}* x^{5}=x^{7}$

Answer: $x^{7}$

Report an Error

Example Question #62 : Algebra

$y^{5}* y^{9}=$

Possible Answers:

$y^{4}$

Cannot be simplified further

$y^{59}$

$y^{14}$

Correct answer:

$y^{14}$

Explanation:

Because the two terms have the same base, they can be multiplied together by adding the exponents:

$y^{5}* y^{9}=y^{14}$

Answer: $y^{14}$

Report an Error

Example Question #63 : Algebra

$z^{3}* z^{6}=$

Possible Answers:

Cannot be simplified further

$z^{6}$

$z^{3}$

$z^{9}$

Correct answer:

$z^{9}$

Explanation:

To simplify the expression, add the exponents and keep the base unchanged:

$z^{3}* z^{6}=z^{9}$

Answer: $z^{9}$

Report an Error

Example Question #64 : Algebra

$w^{10}* w^{10}=$

Possible Answers:

w+20

Cannot be simplified further

20w

$w^{100}$

$w^{20}$

Correct answer:

$w^{20}$

Explanation:

To multiply two terms with the same base and different exponents, add the exponents and leave the base unchanged:

$w^{10}* w^{10}=w^{20}$

Answer: $w^{20}$

Report an Error

View Tutors

Robert
Certified Tutor

University of North Carolina at Chapel Hill, Bachelor in Arts, English. North Carolina Central University, Master of Arts, En...

View Tutors

Yongmao
Certified Tutor

Nankai University, Bachelor of Science, Chemistry. Washington University in St Louis, Doctor of Philosophy, Organic Chemistry.

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in Washington DC, ACT Tutors in Philadelphia, Spanish Tutors in Denver, GMAT Tutors in Denver, Physics Tutors in Atlanta, Calculus Tutors in New York City, Physics Tutors in San Francisco-Bay Area, Chemistry Tutors in Phoenix, French Tutors in Houston, French Tutors in Seattle

Popular Courses & Classes

SSAT Courses & Classes in Philadelphia, GRE Courses & Classes in New York City, LSAT Courses & Classes in Seattle, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Atlanta, GMAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Houston, GMAT Courses & Classes in Houston

Popular Test Prep

GRE Test Prep in Atlanta, GMAT Test Prep in Philadelphia, SAT Test Prep in Los Angeles, SAT Test Prep in Washington DC, LSAT Test Prep in Dallas Fort Worth, SSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Phoenix, LSAT Test Prep in Atlanta, ACT Test Prep in Dallas Fort Worth, GMAT Test Prep in Los Angeles

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

ISEE Middle Level Math : Operations

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #31 : How To Multiply Variables

Example Question #671 : Concepts

Example Question #1267 : Hspt Mathematics

Example Question #32 : How To Multiply Variables

Example Question #31 : Operations

Example Question #32 : Operations

Example Question #61 : Algebra

Example Question #62 : Algebra

Example Question #63 : Algebra

Example Question #64 : Algebra

All ISEE Middle Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: