We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Variables

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

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 14 Next →

Example Question #1 : How To Find The Exponent Of Variables

Simplify:

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

Possible Answers:

$\frac{4z^8}{x^4y^2}$

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

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

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

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

Correct answer:

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

Explanation:

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

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

Apply the exponent within the parentheses and simplify.

$\frac{(2z^3)^2}{(x^2y)^2}$

$\frac{2^2(z^3)^2}{(x^2)^2y^2}$

$\frac{4z^{(3\times 2)}}{x^{(2\times 2)}y^2}$

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

Report an Error

Example Question #971 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify if $x\neq 0,-1$ and $y\neq 0$ .

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

Possible Answers:

2x+1

2x-1

x-1

x+1

Correct answer:

x+1

Explanation:

Begin by factoring the numerator and denominator. can be factored out of each term.

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

can be canceled, since it appears in both the numerator and denomintor.

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

Next, factor the numerator.

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

Simplify.

$\frac{(x+1)(x+1)}{x+1}=x+1$

Report an Error

Example Question #81 : Variables

$\frac{1}{3}+ \sqrt{y}= \frac{2}{5}$

Evaluate .

Possible Answers:

$\frac{121}{225 }$

$\frac{1}{4}$

$\frac{1}{225 }$

$\frac{9}{64}$

Correct answer:

$\frac{1}{225 }$

Explanation:

$\frac{1}{3}+ \sqrt{y}= \frac{2}{5}$

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

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

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

$\sqrt{y} = \frac{6}{1 5} - \frac{ 5}{15}$

$\sqrt{y} = \frac{6- 5}{15}$

$\sqrt{y} = \frac{1}{15}$

$y = (\sqrt{y}) ^{2}= \left (\frac{1}{15} \right )^{2} = \frac{1^{2}}{15 ^{2}} = \frac{1}{225 }$

Report an Error

Example Question #82 : Variables

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

Evaluate .

Possible Answers:

$\frac{1}{4}$

$\frac{9}{64}$

$\frac{1}{225 }$

$\frac{121}{225 }$

Correct answer:

$\frac{121}{225 }$

Explanation:

To solve for the variable isolate it on one side of the equation with all of constants on the other side.

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

First add one third to both sides.

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

$\sqrt{y} = \frac{2}{5} + \frac{1}{3}$

Calculate a common denominator to add the two fractions.

$\sqrt{y} = \frac{3 \cdot 2}{3 \cdot 5} + \frac{1 \cdot 5}{3 \cdot 5}$

$\sqrt{y} = \frac{6}{1 5} + \frac{ 5}{15}$

$\sqrt{y} = \frac{6+ 5}{15}$

$\sqrt{y} = \frac{11}{15}$

Square both sides to solve for y.

$y = (\sqrt{y}) ^{2}= \left (\frac{11}{15} \right )^{2} = \frac{11^{2}}{15 ^{2}} = \frac{121}{225 }$

Report an Error

Example Question #83 : Variables

Simplify the following:

(7t^6h^4b^9)^3

Possible Answers:

$343t^{18}h^{12}b^{27}$

$21t^{9}h^{7}b^{12}$

$343t^{9}h^{7}b^{12}$

$11t^{9}h^{7}b^{12}$

Correct answer:

$343t^{18}h^{12}b^{27}$

Explanation:

Simplify the following:

(7t^6h^4b^9)^3

Let's recall the rules for distributing exponents.

We treat coefficients (like the 7) like regular numbers and raise them to the new exponent.

We deal with variables (like the t, h, and b) by multiplying their current exponent by the new exponent.

Doing so yields:

$7^3t^{6*3}h^{3*4}b^{3*9}$

Simplify to get:

$343t^{18}h^{12}b^{27}$

Report an Error

Example Question #81 : Variables

$a^{3} = -10$

Evaluate $(2a) ^{6}$ .

Possible Answers:

-6,400

6,400

200

Correct answer:

6,400

Explanation:

By the Power of a Power Principle,

$(a^{3} ) ^{2} =a ^{3 \cdot 2} = a ^{6}$

$a ^{6} = (a^{3} ) ^{2} = (-10) ^{2} =+ (10 ^{2} )= 100$

Also, by the Power of a Product Principle,

$(2a) ^{6} = 2^{6} \cdot a ^{6}$

$2 ^{6} = 64$ , so, substituting,

$(2a) ^{6} = 64 ( 100 ) = 6,400$ .

Report an Error

Example Question #85 : Variables

$t ^{3} = -8$

$u^{9} = -12$

Evaluate $(tu) ^{9}$ .

Possible Answers:

6,144

288

-6,144

Correct answer:

6,144

Explanation:

By the Power of a Product Principle,

$(tu) ^{9} = t ^{9} \cdot u ^{9}$

Also, by the Power of a Power Principle,

$(t^{3} ) ^{3} =t ^{3 \cdot 3} = t^{9}$

Combining these ideas, then substituting:

$(tu) ^{9} = (t^{3} ) ^{3} \cdot u ^{9}$

$= (-8) ^{3} \cdot (-12)$

$= (-8^{3} ) \cdot (-12)$

$= (-512 ) \cdot (-12)$

$= +(512 \cdot 12)$

=6,144

Report an Error

Example Question #1 : How To Subtract Exponential Variables

Simplify the expression:

$7x^{3} - 5x^{2} + 9x^{3}$

Possible Answers:

$16 x^{3} - 5x^{2}$

$2x^{2} + 9x^{3}$

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

The expression cannot be simplified further.

$11x^{5}$

Correct answer:

$16 x^{3} - 5x^{2}$

Explanation:

Group, then collect like terms:

$7x^{3} - 5x^{2} + 9x^{3}$

$=7x^{3} + 9x^{3} - 5x^{2}$

$=\left ( 7 + 9 \right )x^{3} - 5x^{2}$

$=16x^{3} - 5x^{2}$

Report an Error

Example Question #2 : How To Subtract Exponential Variables

Simplify:

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

Possible Answers:

-8xy

8xy

$\frac{2x^{2}+8y^{2}}{xy}$

Correct answer:

Explanation:

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

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

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

$=\frac{8xy}{xy} = 8$

Report an Error

Example Question #3 : How To Subtract Exponential Variables

Assume that $x \neq 0$ . Which of the following expressions is equivalent to:

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

Possible Answers:

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

$3 + \frac{ 3 }{x}$

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

$2 + \frac{ 2 }{x}$

Correct answer:

$3 + \frac{ 3 }{x}$

Explanation:

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

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

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

$= \frac{3x^{2} + 3x }{x^{2}}$

$= \frac{3x^{2} }{x^{2}} + \frac{ 3x }{x^{2}}$

$=3 + \frac{ 3 }{x}$

Report an Error

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 14 Next →

View Tutors

Aaron
Certified Tutor

Portland State University, Bachelors, Economics. Portland State University, Masters, Environmental and Resource Management.

View Tutors

Gregory
Certified Tutor

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

View Tutors

Lazaro
Certified Tutor

Miami Dade College, Bachelor of Engineering, Computer Hardware Engineering.

All ISEE Upper Level Math Resources

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

Popular Subjects

SAT Tutors in Atlanta, GMAT Tutors in Seattle, SSAT Tutors in San Diego, Reading Tutors in San Francisco-Bay Area, Chemistry Tutors in San Diego, GMAT Tutors in Miami, Physics Tutors in Seattle, Chemistry Tutors in Seattle, GRE Tutors in Houston, Reading Tutors in Atlanta

Popular Courses & Classes

ISEE Courses & Classes in Washington DC, GRE Courses & Classes in Boston, ISEE Courses & Classes in Boston, GRE Courses & Classes in Los Angeles, SSAT Courses & Classes in Denver, ACT Courses & Classes in Chicago, LSAT Courses & Classes in Denver, GRE Courses & Classes in New York City, LSAT Courses & Classes in Atlanta, ISEE Courses & Classes in New York City

Popular Test Prep

SAT Test Prep in Miami, SAT Test Prep in Dallas Fort Worth, SAT Test Prep in Houston, ACT Test Prep in Houston, ACT Test Prep in Philadelphia, GRE Test Prep in Los Angeles, ACT Test Prep in Phoenix, GRE Test Prep in Houston, SAT Test Prep in Boston, ACT Test Prep in Chicago

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

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Exponent Of Variables

Example Question #971 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #81 : Variables

Example Question #82 : Variables

Example Question #83 : Variables

Example Question #81 : Variables

Example Question #85 : Variables

Example Question #1 : How To Subtract Exponential Variables

Example Question #2 : How To Subtract Exponential Variables

Example Question #3 : How To Subtract 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: