Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : ISEE Upper Level (grades 9-12) Mathematics Achievement

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 #1011 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Multiply the following:

$x^5 \cdot x^2$

Possible Answers:

$2x^{10}$

x^7

2x^7

$x^{10}$

$2x^{12}$

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

Example Question #23 : How To Multiply Exponential Variables

Multiply the following:

$b^4 \cdot b^2$

Possible Answers:

b^6

$b^{42}$

b^8

b^2

b^4

Correct answer:

b^6

Explanation:

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

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

Now, let’s combine the following:

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

$b^4 \cdot b^2 = b^{6}$

Report an Error

Example Question #24 : How To Multiply Exponential Variables

Solve the following:

$3y^3 \cdot 4y^2$

Possible Answers:

7y^6

12y

7y^5

12y^6

12y^5

Correct answer:

12y^5

Explanation:

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

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

Also, we will multiply coefficients like normal.

So, we get

$3y^3 \cdot 4y^2$

$12(y^3 \cdot y^2)$

$12(y^{3+2})$

12y^5

Report an Error

Example Question #311 : Algebraic Concepts

Simplify the following expression:

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

Possible Answers:

$108x^{10}y^{24}$

$98x^8y^{10}$

$108x^8y^{10}$

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

$108x^8y^{16}$

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 #1011 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify the following:

$\frac{p^{6}}{p^{3}}$

Possible Answers:

$p^{9}$

$p^{2}$

$\frac{p}{2}$

$p^{3}$

Correct answer:

$p^{3}$

Explanation:

To divide a variable with an exponent, you can write out all the multiplies, which for this question would look like:

$\frac{pppppp}{ppp}$

Then cancel out the matching p's, leaving:

$ppp=p^{3}$

Or, if the top and bottom are the same variable, you can simply subtract the bottom exponent from the top exponent.

$p^{6-3}=p^{3}$

Report an Error

Example Question #1012 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify the following:

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

Possible Answers:

$y^{0.4}$

$y^{3}$

$\frac{1}{3y}$

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

Correct answer:

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

Explanation:

To divide variables with exponents, either:

Write out the multiplies, then reduce

$\frac{yy}{yyyyy}=\frac{1}{y^{3}}$

or subtract the bottom exponent from the top, like so

$y^{2-5}=y^{-3}=\frac{1}{y^{3}}$

Remember, negative exponent means dividing. $y^{-3}$ would also be correct, but you should know that is equivalent to $\frac{1}{y^{3}}$

Report an Error

Example Question #1013 : Isee Upper Level (Grades 9 12) Mathematics Achievement

If $x\neq -1,0,1$ , simplify:

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

Possible Answers:

3(x+1)

3(x^2+1)

3(x^2-1)

3(x-1)

2(x^2+1)

Correct answer:

3(x^2+1)

Explanation:

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

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

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

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

=3(x^2+1)

Report an Error

Example Question #1013 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify:

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

$\frac{x^6y^2z^3}{x^3y^4z^3}=x^{6-3}y^{2-4}z^{3-3}=x^3y^{-2}z^0=\frac{x^3}{y^2}$

Report an Error

Example Question #5 : How To Divide Exponential Variables

Simplify if $xy\neq \pm 2$ .

$\frac{x^4y^4-4x^2y^2}{(xy+2)(xy-2)}$

Possible Answers:

x^2y^2

-xy

$x^{-1}y^2$

-x^2y^2

Correct answer:

x^2y^2

Explanation:

Start by factoring the numerator. x^2y^2 can be removed from each term.

$\frac{x^4y^4-4x^2y^2}{(xy+2)(xy-2)}=\frac{x^2y^2(x^2y^2-4)}{(xy+2)(xy-2)}$

Next, expand the denominator.

$\frac{x^2y^2(x^2y^2-4)}{(xy+2)(xy-2)}=\frac{x^2y^2(x^2y^2-4)}{x^2y^2-4}$

Simplify by canceling terms.

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

Report an Error

Example Question #2 : How To Divide Exponential Variables

Simplify:

$\frac{2x^{-7}}{(3x)^{-2}}$

Possible Answers:

$\frac{18}{x^5}$

$\frac{18}{x^4}$

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

18x^5

9x^5

Correct answer:

$\frac{18}{x^5}$

Explanation:

In the denominator, apply the exponent to the terms in parentheses.

$\frac{2x^{-7}}{(3x)^{-2}}=\frac{2x^{-7}}{(3^{-2}) (x^{-2})}$

Terms with negative exponents can be inverted within the fraction to eliminate the negative.

$\frac{2x^{-7}}{(3^{-2}) (x^{-2})}=\frac{2(3^2)(x^2)}{x^7}$

Simplify by canceling variables and mulitplying.

$\frac{2(3^2)(x^2)}{x^7}=\frac{18x^2}{x^7}=\frac{18}{x^5}$

Report an Error

View Tutors

Mike Bahaa
Certified Tutor

Concordia University-Ann Arbor, Master of Arts Teaching, Mathematics Teacher Education.

View Tutors

Reza
Certified Tutor

University of Sherbrooke, Doctor of Philosophy, Mathematics. University of Manitoba, Master of Science, Mathematics.

View Tutors

Ana
Certified Tutor

Grand Canyon University, Bachelors, Education. Grand Canyon University, Masters, Education.

All ISEE Upper Level Math Resources

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

Popular Subjects

Chemistry Tutors in Houston, Calculus Tutors in Houston, Physics Tutors in Phoenix, SAT Tutors in Phoenix, Reading Tutors in Washington DC, ISEE Tutors in Los Angeles, Biology Tutors in San Diego, Computer Science Tutors in San Francisco-Bay Area, Spanish Tutors in Miami, Statistics Tutors in Washington DC

Popular Courses & Classes

Spanish Courses & Classes in Chicago, GMAT Courses & Classes in San Diego, GMAT Courses & Classes in Phoenix, SSAT Courses & Classes in Phoenix, GRE Courses & Classes in Denver, SAT Courses & Classes in Atlanta, Spanish Courses & Classes in Seattle, MCAT Courses & Classes in Los Angeles, MCAT Courses & Classes in New York City, SSAT Courses & Classes in Miami

Popular Test Prep

GMAT Test Prep in New York City, SAT Test Prep in Dallas Fort Worth, MCAT Test Prep in New York City, SAT Test Prep in Seattle, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Los Angeles, GRE Test Prep in Philadelphia, SSAT Test Prep in Seattle, GRE Test Prep in Miami, ACT Test Prep in Denver

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 : ISEE Upper Level (grades 9-12) Mathematics Achievement

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1011 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #23 : How To Multiply Exponential Variables

Example Question #24 : How To Multiply Exponential Variables

Example Question #311 : Algebraic Concepts

Example Question #1011 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1012 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1013 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1013 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #5 : How To Divide Exponential Variables

Example Question #2 : How To Divide Exponential 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: