GRE Math : Exponential Operations

Study concepts, example questions & explanations for GRE Math

Create An Account

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Exponential Operations

Evaluate:

$y=\frac{3^{13}-9^{5}}{\left ( \frac{1}{27} \right )^{-3}}$

Possible Answers:

$\dpi{100} \small 24$

$\dpi{100} \small 78$

$\dpi{100} \small 30$

$\dpi{100} \small 81$

$\dpi{100} \small 27$

Correct answer:

$\dpi{100} \small 78$

Explanation:

Can be simplified to:

Capture2

Report an Error

Example Question #32 : Exponential Operations

Simplify the following expression.

$\frac{((x^4)^{-7})}{(x^2*x^4)}$

Possible Answers:

$\frac{1}{x^{22}}$

$x^{22}$

$\frac{1}{x^{34}}$

$x^{34}$

$\textup{This expression can't be simplified any further}$

Correct answer:

$\frac{1}{x^{34}}$

Explanation:

To solve this problem, we must first understand some of the basic concepts of exponents. When multiplying exponents with the same base, one would simply add the powers together with the same base to obtain the result. For example, $x^a*x^b=x^{a+b}$ .

When raising exponents to a certain power, one would simply multiply the power the exponent is being raised to with the exponent itself to obtain the new exponent. The base also gets raised to the same power as it normally would and the new exponent gets put on afterward. For example $({x^a})^{b}=x^{a*b}$ .

Now that we have covered the basic concepts of exponent manipulation, we can now solve the problem. The top part of the expression give to us is $((x^4)^{-7})$ . As we have stated before, when an exponent is raised to a certain power, you simply multiply the power and the exponent together. This results in $x^{4*-7}=x^{-28}$ .

The new expression becomes $\frac{x^{-28}}{(x^2*x^4)}$ .

Solving for the denominator of the equation, we previously stated that when multiplying exponents together with the same base, we simply add the exponents together and keep the same base. Therefore $(x^2*x^4)=x^{2+4}=x^6$ .

The new expression becomes $\frac{x^{-28}}{x^6}$ , however $x^{-28}=\frac{1}{x^{28}}$ , therefore the expression becomes $\frac{1}{x^{28}*x^{6}}=\frac{1}{x^{34}}$ .

Report an Error

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in San Francisco-Bay Area, SSAT Tutors in New York City, Algebra Tutors in New York City, Calculus Tutors in New York City, Computer Science Tutors in Seattle, ISEE Tutors in New York City, SSAT Tutors in Phoenix, ISEE Tutors in Chicago, Spanish Tutors in San Francisco-Bay Area, SSAT Tutors in Washington DC

Popular Courses & Classes

GMAT Courses & Classes in Los Angeles, ACT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in New York City, ISEE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Washington DC, LSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in San Diego, ISEE Courses & Classes in Seattle

Popular Test Prep

SSAT Test Prep in Seattle, ACT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in Denver, LSAT Test Prep in Denver, ISEE Test Prep in Washington DC, GRE Test Prep in San Francisco-Bay Area, GRE Test Prep in San Diego, GMAT Test Prep in Atlanta, ISEE 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)

Email address:
Your name:
Feedback:

GRE Math : Exponential Operations

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #31 : Exponential Operations

Example Question #32 : Exponential Operations

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details