Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Variables and Exponents

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

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #113 : Variables

Simplify:

2(x^2y^3)^2(3xy^2)^3

Possible Answers:

$27x^7y^{13}$

$54x^7y^{12}$

$x^7y^{12}$

$2x^7y^{13}$

Correct answer:

$54x^7y^{12}$

Explanation:

First, simplify all of the exponents. When the exponent is outside of the parantheses, multiply it by the exponents inside so that you get: 2(x^4y^6)(3^3x^3y^6) . Multiply 3^3 so that you get 27. Then, multiply like terms. First, multilpy 2 by 27 so that you get 54. Then, multiply the x terms. Remember, when bases are the same, add the exponents: $x^4\cdot x^3=x^7$ . Then, multiply the y terms: $y^6\cdot y^6=y^{12}$ . Then, multiply all of the terms together so that you get $54x^7y^{12}$ .

Report an Error

Example Question #114 : Variables

Simplify:

$\frac{4x^{3}}{y} \cdot \frac{y^{5}}{8x} \cdot xy$

Possible Answers:

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

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

$\frac{ x^{2 } y^{4} }{2 }$

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

Correct answer:

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

Explanation:

$\frac{4x^{3}}{y} \cdot \frac{y^{5}}{8x} \cdot xy$

$= \frac{4x^{3}}{y} \cdot \frac{y^{5}}{8x} \cdot \frac{xy}{1}$

$= \frac{4x^{3} \cdot y^{5} \cdot xy }{y \cdot 8x \cdot 1 }$

$= \frac{4x^{3+1 } \cdot y^{5+1} }{8xy }$

$= \frac{4x^{4 } \cdot y^{6} }{8xy }$

$= \frac{ x^{4-1 } \cdot y^{6-1} }{2 }$

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

Report an Error

Example Question #51 : Variables And Exponents

Simplify the following expression:

(9x^5y^2)(12x^3y^8)

Possible Answers:

$108x^{15}y^{10}$

$108x^8y^{16}$

$108x^8y^{10}$

$98x^8y^{10}$

Correct answer:

$108x^8y^{10}$

Explanation:

Simplify the following expression:

(9x^5y^2)(12x^3y^8)

To combine these, we need to multiply our coefficients and our variables.

First, multiply the coefficients

9*12=108

Next, multiply our variables by adding the exponent:

$(x^5y^2)(x^3y^8)=x^{5+3}y^{2+8}=x^8y^{10}$

So, we put it all together to get:

$108x^8y^{10}$

Report an Error

Example Question #52 : Variables And Exponents

Simplify the following:

$a^2 \cdot a^4$

Possible Answers:

a^6

a^8

a^2

$a^{12}$

a^4

Correct answer:

a^6

Explanation:

When multiply variables with exponents, we will use the following formula:

$a^x \cdot a^y = a^{x+y}$

So, we can write the problem like this:

$a^2 \cdot a^4 = a^{2+4}$

$a^2 \cdot a^4 = a^6$

Report an Error

Example Question #53 : Variables And Exponents

Combine the following:

$x^3 \cdot x^7$

Possible Answers:

$2x^{10}$

$x^{10}$

$x^{21}$

x^4

$x^{37}$

Correct answer:

$x^{10}$

Explanation:

To combine variables with exponents, we will use the following formula:

$x^a \cdot x^b = x^{a+b}$

Now, let’s combine the following:

$x^3 \cdot x^7 = x^{3+7}$

$x^3 \cdot x^7 = x^{10}$

Report an Error

Example Question #303 : Algebraic Concepts

Combine the following:

$a^5 \cdot b^2 \cdot a^7 \cdot b^4$

Possible Answers:

$a^{12} \cdot b^6$

$ab^{18}$

$ab^{43}$

$2a^{12} \cdot 2b^6$

$a^{35} \cdot b^8$

Correct answer:

$a^{12} \cdot b^6$

Explanation:

When combining variables with exponents, we can only combine like variables.

When multiply variables with exponents, we add the exponents. In other words:

$a^x \cdot a^y = a^{x+y}$

So, we get

$a^5 \cdot b^2 \cdot a^7 \cdot b^4$

$a^5 \cdot a^7 \cdot b^2 \cdot b^4$

$a^{5+7} \cdot b^{2+4}$

$a^{12} \cdot b^6$

Report an Error

Example Question #54 : Variables And Exponents

Simplify:

$b^2 \cdot b^7$

Possible Answers:

$b^{14}$

$b^{27}$

b^9

b^5

b^7

Correct answer:

b^9

Explanation:

To simplify, we will use the following formula:

$x^a \cdot x^b = x^{a+b}$

So, given the problem, we get

$b^2 \cdot b^7 = b^{2+7}$

$b^2 \cdot b^7 = b^9$

Report an Error

Example Question #55 : Variables And Exponents

Combine the following:

$b^4 \cdot b^5 \cdot b$

Possible Answers:

$b^{10}$

$3b^{10}$

b^9

$b^{20}$

3b^9

Correct answer:

$b^{10}$

Explanation:

To multiply terms with exponents, we will use the following formula:

$a^x \cdot a^y = a^{x+y}$

So, we get

$b^4 \cdot b^5 \cdot b$

$b^4 \cdot b^5 \cdot b^1$

$b^{4+5+1}$

$b^{10}$

Report an Error

Example Question #121 : Variables

Simplify the following expression:

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

Possible Answers:

64x^4-6x^6

18x^6

70x^6

64x^5+6x^6

Correct answer:

70x^6

Explanation:

Simplify the following expression:

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

Let's begin with the first term.

Because we are raising the whole part to the third, we need to cube each piece, the 4 and the x squared.

4^3(x^2)^3+6x^6=64x^6+6x^6

Next, simply add our two terms to get our answer

64x^6+6x^6=70x^6

Report an Error

Example Question #122 : Variables

Multiply the following:

$x^5 \cdot x^2$

Possible Answers:

$2x^{10}$

$x^{10}$

2x^7

$2x^{12}$

x^7

Correct answer:

x^7

Explanation:

To multiply like variables with exponents, we will use the following formula:

$a^x \cdot a^y = a^{x+y}$

So, we get

$x^5 \cdot x^2 = x^{5+2}$

$x^5 \cdot x^2 = x^7$

Report an Error

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Jaleesa
Certified Tutor

Pomona College, Bachelors, Africana Studies.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in San Francisco-Bay Area, Math Tutors in Los Angeles, Math Tutors in Miami, Computer Science Tutors in Philadelphia, French Tutors in Atlanta, Algebra Tutors in Philadelphia, Statistics Tutors in Dallas Fort Worth, Statistics Tutors in Philadelphia, GRE Tutors in Denver, SSAT Tutors in Houston

Popular Courses & Classes

SSAT Courses & Classes in San Diego, MCAT Courses & Classes in Los Angeles, SAT Courses & Classes in Seattle, GMAT Courses & Classes in New York City, LSAT Courses & Classes in Miami, GMAT Courses & Classes in Boston, LSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Atlanta

Popular Test Prep

LSAT Test Prep in Washington DC, LSAT Test Prep in Houston, GRE Test Prep in Boston, MCAT Test Prep in New York City, GMAT Test Prep in San Diego, GRE Test Prep in San Francisco-Bay Area, SAT Test Prep in Houston, SSAT Test Prep in Washington DC, SAT Test Prep in Boston, GRE 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

ISEE Upper Level Math : Variables and Exponents

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #113 : Variables

Example Question #114 : Variables

Example Question #51 : Variables And Exponents

Example Question #52 : Variables And Exponents

Example Question #53 : Variables And Exponents

Example Question #303 : Algebraic Concepts

Example Question #54 : Variables And Exponents

Example Question #55 : Variables And Exponents

Example Question #121 : Variables

Example Question #122 : Variables

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: