We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : How to multiply exponential 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

Example Question #1 : How To Multiply Exponential Variables

Simplify the following:

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

Possible Answers:

$z^{3}x^{6}y^{4}$

$z^{3}xy^{3}$

None of the other answers

$(zxy)^{13}$

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

Correct answer:

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

Explanation:

To multiply variables with exponents, add the exponents. With multiple variables, simply add the exponents for each different variable.

Simplified:

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

Report an Error

Example Question #2 : How To Multiply Exponential Variables

Simplify the following:

$(3py^{2})(4p^{4})$

Possible Answers:

$7py^{8}$

$12p^{5}y^{2}$

None of the other answers

$7p^{5}y^{2}$

$12(py)^{8}$

Correct answer:

$12p^{5}y^{2}$

Explanation:

To multiply variables with exponents, add the exponents. When there are constants mixed in, multiply the constants separately and put back in the final result:

$(3py^{2})(4p^{4})$

$3\times4\times p^{1+4}\times y^{2}$

Report an Error

Example Question #3 : How To Multiply Exponential Variables

Simplify the following:

$z^{2}\times z^{5}$

Possible Answers:

$z^{3}$

$z^{7}$

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

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

$z^{10}$

Correct answer:

$z^{7}$

Explanation:

To multiply variables with exponents, add the exponents. So,

$z^{2}\times z^{5}=z^{7}$

A longer way would be to write out all the multiplies the exponent tells us to do. This is a little clearer on why adding the exponents works but takes longer and isn't necessary once you understand the process.

$z^{2}\times z^{5}= zzzzzzz= z^{7}$

Report an Error

Example Question #4 : How To Multiply Exponential Variables

Factor completely:

$x^{3} - 3x^{2}+ 4x$

Possible Answers:

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

$\left(x ^{2}- 2 \right ) \left (x - 2 \right )$

$x\left (x - 2 \right )\left (x - 2 \right )$

$x\left (x - 4 \right )\left (x - 1 \right )$

$x\left (x^{2} - 3x+ 4 \right )$

Correct answer:

$x\left (x^{2} - 3x+ 4 \right )$

Explanation:

is the greatest common factor of each term, so distribute it out:

$x^{3} - 3x^{2}+ 4x$

$= x \left (\frac{ x^{3} }{x}- \frac{3x^{2} }{x}+ \frac{4x}{x} \right )$

$= x \left (x^{2}- 3x + 4 \right )$

We try to factor $x^{2}- 3x + 4$ by finding two integers with product 4 and sum . However, both of our possible factor pairs fail, since -2 + (-2) = -4 and -1+ (-4) = -5 .

$x \left (x^{2}- 3x + 4 \right )$ is the complete factorization.

Report an Error

Example Question #4 : How To Multiply Exponential Variables

Multiply:

$\left ( x -3y + 1\right ) \left ( x - 3y - 1\right )$

Possible Answers:

$x^{2} + 3xy -9y ^{2} - 1$

$x^{2} + 6xy -9y ^{2} - 1$

$x^{2} - 6xy +9y ^{2} - 1$

$x^{2} +9y ^{2} - 1$

$x^{2} - 3xy +9y ^{2} - 1$

Correct answer:

$x^{2} - 6xy +9y ^{2} - 1$

Explanation:

This can be achieved by using the pattern of difference of squares:

$\left ( x -3y + 1\right ) \left ( x - 3y - 1\right )$

$=\left [ \left ( x -3y \right ) + 1\right ] \left \left[( x - 3y \right ) - 1\right ]$

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

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

Applying the binomial square pattern:

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

$= x^{2} - 6xy +9y ^{2} - 1$

Report an Error

Example Question #5 : How To Multiply Exponential Variables

Factor completely:

$4 y^{2} - 100 y$

Possible Answers:

4y (y - 25)

4 (y + 5) (y - 5)

2 (y + 10) (4y - 5)

$4 (y - 5)^{2}$

$4y ^{2}(y - 25)$

Correct answer:

4y (y - 25)

Explanation:

The greatest common factor of the terms in $4 y^{2} - 100 y$ is , so factor that out:

$4 y^{2} - 100 y$

$= 4y\left ( \frac{4 y^{2}}{4y} - \frac{100 y}{4y} \right )$

$= 4y\left (y - 25 \right )$

Since all factors here are linear, this is the complete factorization.

Report an Error

Example Question #6 : How To Multiply Exponential Variables

Exponentiate:

$\left (x + 0.5y \right) ^{3}$

Possible Answers:

$x^{3} + x^{2} y + 0.5 \ x y ^{2} + 0.125 y ^{3}$

$x^{3} + 1.5 x^{2} y + 0.75 \ x y ^{2} + 0.125 y ^{3}$

$x^{3} + 0.125 y ^{3}$

$x^{3} + 0.5 x^{2} y + 0.25 \ x y ^{2} + 0.125 y ^{3}$

$x^{3} + 1.5 x^{2} y + 0.75 \ x y ^{2} + 1.25 y ^{3}$

Correct answer:

$x^{3} + 1.5 x^{2} y + 0.75 \ x y ^{2} + 0.125 y ^{3}$

Explanation:

The cube of a sum pattern can be applied here:

$\left (x + 0.5y \right) ^{3}$

$= x^{3} + 3 \cdot x^{2}\cdot 0.5y + 3 \cdot x \cdot\left (0.5y \right) ^{2} + \left (0.5y \right) ^{3}$

$= x^{3} + 3\cdot 0.5 \cdot x^{2} \cdot y + 3 \cdot 0.5^{2} \cdot x \cdot y ^{2} + 0.5^{3} \cdot y ^{3}$

$= x^{3} + 3 \cdot 0.5 x^{2} y + 3 \cdot 0.25 \ x y ^{2} + 0.125 y ^{3}$

$= x^{3} + 1.5 x^{2} y + 0.75 \ x y ^{2} + 0.125 y ^{3}$

Report an Error

Example Question #7 : How To Multiply Exponential Variables

Write in expanded form:

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

Possible Answers:

$8x^{3} + \frac{1}{8}$

$8x^{3} + 6 x^{2} + \frac{3}{2} x + \frac{1}{8}$

$8x^{3} + x^{2} +x + \frac{1}{8}$

$8x^{3} + 2 x^{2} + \frac{1}{2} x + \frac{1}{8}$

$8x^{3} + 6 x^{2} + 3x + \frac{1}{8}$

Correct answer:

$8x^{3} + 6 x^{2} + \frac{3}{2} x + \frac{1}{8}$

Explanation:

The cube of a sum pattern can be applied here:

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

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

$= 2^{3}\cdot x^{3} + 3\cdot 2^{2}\cdot \frac{1}{2} \cdot x^{2} + 3\cdot2 \cdot \left (\frac{1}{2} \right ) ^{2} \cdot x \left + \left ( \frac{1}{2} \right ) ^{3}$

$= 8x^{3} + 6 x^{2} + \frac{3}{2} x + \frac{1}{8}$

Report an Error

Example Question #8 : How To Multiply Exponential Variables

Factor completely:

$x ^{2} - 11x + 20$

Possible Answers:

(x - 4)(x - 5)

The expression cannot be factored.

(x - 2)(x - 10)

(x - 4)(x + 5)

(x + 2)(x - 10)

Correct answer:

The expression cannot be factored.

Explanation:

A trinomial with leading coefficient $x^{2}$ can be factored by looking for two integers to fill in the boxes:

$(x + \square )(x + \square )$ .

The numbers should have product 20 and sum . However, all of the possible factor pairs fail:

-1 + (-20) = -21

-2 + (-10) = -12

-4 + (-5) = -9

The polynomial is prime.

Report an Error

Example Question #9 : How To Multiply Exponential Variables

Factor completely:

$4x^{2} - 36x+ 81$

Possible Answers:

(4x-3)(x-27)

$(2x-9)^{2}$

(4x-9)(x-9)

(x-3)(4x-27)

(2x-3)(2x-27)

Correct answer:

$(2x-9)^{2}$

Explanation:

$4x^{2} - 36x+ 81$ can be seen to be a perfect square trinomial by taking the square root of the first and last terms, multiplying their product by 2, then comparing it to the second term:

$4x^{2} = \left ( 2x\right )^{2}$

$81 = 9^{2}$

$2 \cdot2x\cdot9= 36x$

Therefore,

$4x^{2} - 36x+ 81$

$=\left ( 2x \right ) ^{2} -2 \cdot 2 x \cdot9+ 9 ^{2}$

$=(2x-9)^{2}$

Report an Error

View Tutors

Reza
Certified Tutor

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

View Tutors

Gabby
Certified Tutor

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

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

ACT Tutors in Atlanta, ISEE Tutors in New York City, Math Tutors in Seattle, Chemistry Tutors in Phoenix, MCAT Tutors in New York City, Statistics Tutors in Boston, Algebra Tutors in Denver, ISEE Tutors in San Francisco-Bay Area, Biology Tutors in Denver, Physics Tutors in New York City

Popular Courses & Classes

Spanish Courses & Classes in Phoenix, ISEE Courses & Classes in Seattle, SAT Courses & Classes in Phoenix, SAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Diego, ISEE Courses & Classes in Philadelphia, LSAT Courses & Classes in Phoenix, GRE Courses & Classes in Denver, Spanish Courses & Classes in New York City, MCAT Courses & Classes in Houston

Popular Test Prep

LSAT Test Prep in Philadelphia, SSAT Test Prep in Seattle, ISEE Test Prep in Atlanta, SSAT Test Prep in Boston, SAT Test Prep in Phoenix, GRE Test Prep in Boston, MCAT Test Prep in Philadelphia, GRE Test Prep in Los Angeles, ISEE Test Prep in San Francisco-Bay Area, ISEE 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 Upper Level Math : How to multiply exponential variables

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Multiply Exponential Variables

Example Question #2 : How To Multiply Exponential Variables

Example Question #3 : How To Multiply Exponential Variables

Example Question #4 : How To Multiply Exponential Variables

Example Question #4 : How To Multiply Exponential Variables

Example Question #5 : How To Multiply Exponential Variables

Example Question #6 : How To Multiply Exponential Variables

Example Question #7 : How To Multiply Exponential Variables

Example Question #8 : How To Multiply Exponential Variables

Example Question #9 : How To Multiply 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: