Call Now to Set Up Tutoring:

(888) 888-0446

Create an account to track your scores
and create your own practice tests:

Create an Account Create a Practice Test

All SAT Mathematics Resources

137 Practice Tests Question of the Day Flashcards Learn by Concept

Want to review SAT Mathematics but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different SAT Mathematics flashcards! Our SAT Mathematics flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous SAT Mathematics flashcards.

Flashcards: Identifying Properties of Roots & Exponents

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

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

$x^{3}y^{3}$

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

Report an Error Copyright Notice

Flashcards: Identifying Properties of Roots & Exponents

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

Your answer:

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

Your answer:

$x^{3}y^{3}$

Your answer:

Correct answer:

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

Explanation:

Whenever you exponential expressions in both the numerator and denominator of a fraction, your first inclination might be to quickly simplify the expressions by canceling terms out in the numerator and denominator.

However, remember to follow the order of operations: you must simplify the numerator and denominator separately to revolve the exponents raised to exponents problem before you can look to cancel terms in the numerator and denominator.

If you consider the numerator, $(x^{4}y^{3})^{-2}$ , you should recognize that, because there is no addition or subtraction within the parentheses, that you can simplify this expression by multiplying each exponent within the parentheses by to get:

$x^{-8}y^{-6}$ .

Similarly, you can simplify the denominator, $(x^{3}y^{2})^{-2}$ by multiplying each exponent within the parentheses by to get:

$x^{-12}y^{-8}$ .

You can then recombine the numerator and denominator to get $\frac{x^{-8}y^{-6}}{x^{-12}y^{-8}}$ . Notice that you now have simple division. Remember that anytime you want to combine two exponential expressions with a common base that are being divided, you simply need to subtract the exponents. If you do, you get:

$x^{-8-(-12)}y^{-6-(-8)}$ , which simplifies to $x^{4}y^{2}$ .

Remember that if you forgot any of the rules, such as how to combine exponents with common bases that are being divided or whether you add or multiply when raising a power to a power, that you can always remind yourself how the rules work by testing small numbers.

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)

View Tutors

Anjali
Certified Tutor

Delhi University, Bachelor of Science, Physics. Kumuan University, Master of Science, Physics.

View Tutors

Pankaj
Certified Tutor

University of Delhi, Electrical Engineer, Electrical Engineering. Columbia University in the City of New York, Master of Arts...

View Tutors

Bhavana
Certified Tutor

Indian Institute of Science Education and Research, Tirupati, Master's/Graduate, Physics and biology .

Popular Subjects

Spanish Tutors in San Francisco-Bay Area, Biology Tutors in San Francisco-Bay Area, SSAT Tutors in Atlanta, Spanish Tutors in San Diego, Statistics Tutors in San Diego, Chemistry Tutors in Phoenix, Spanish Tutors in New York City, Reading Tutors in Washington DC, ISEE Tutors in New York City, English Tutors in Houston

Popular Courses & Classes

SSAT Courses & Classes in Miami, GRE Courses & Classes in Atlanta, SAT Courses & Classes in Boston, LSAT Courses & Classes in Washington DC, LSAT Courses & Classes in New York City, SSAT Courses & Classes in Houston, SAT Courses & Classes in Chicago, SSAT Courses & Classes in New York City, LSAT Courses & Classes in Miami, LSAT Courses & Classes in Seattle

Popular Test Prep

SAT Test Prep in Chicago, ISEE Test Prep in Philadelphia, SAT Test Prep in Los Angeles, MCAT Test Prep in San Diego, SAT Test Prep in Boston, LSAT Test Prep in Phoenix, LSAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Seattle, SSAT Test Prep in Denver, ACT Test Prep in Miami

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores
and create your own practice tests:

All SAT Mathematics Resources

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback:

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores and create your own practice tests:

All SAT Mathematics Resources

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Create an account to track your scores
and create your own practice tests: