GRE Math : Exponents

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 #3 : Exponents And Rational Numbers

Solve for

$2^{x+1}=128$

Possible Answers:

Correct answer:

Explanation:

Recall that 128=2^7 .

With same base, we can write this equation:

x+1=7 .

By subtracting on both sides, x=6 .

Report an Error

Example Question #2 : Exponents And Rational Numbers

Solve for .

$2^{x^2+4}=32$

Possible Answers:

-1, 1

Correct answer:

-1, 1

Explanation:

Since 32=2^5 we can rewrite the expression.

With same base, let's set up an equation of x^2+4=5 .

By subtracting on both sides, we get x^2=1 .

Take the square root of both sides we get BOTH and .

Report an Error

Example Question #8 : Exponents And Rational Numbers

Solve for .

5^x=25^4

Possible Answers:

Correct answer:

Explanation:

They don't have the same base, however: 25=5^2 .

Then 25^4=(5^2)^4 . You would multiply the and the instead of adding.

$2\cdot 4=8$ .

x=8

Report an Error

Example Question #9 : Exponents And Rational Numbers

Solve for .

$4^{2x}=16^6$

Possible Answers:

Correct answer:

Explanation:

There are two ways to go about this.

Method

They don't have the same bases however: 16=4^2 . Then 16^6=(4^2)^6

You would multiply the and the instead of adding. We have $2\cdot 6=2x$

Divide on both sides to get x=6 .

Method :

We can change the base from to 16.

$4^{2x}=(4^2)^x=16^x$

This is the basic property of the product of power exponents.

We have the same base so basically x=6 .

Report an Error

Example Question #10 : Exponents And Rational Numbers

Solve for .

1024^x=2

Possible Answers:

$\frac{1}{10}$

$-\frac{1}{10}$

Correct answer:

$\frac{1}{10}$

Explanation:

Since we can write $1024^x=(2^{10})^x$ .

With same base we can set up an equation of 10x=1

Divide both sides by and we get $x=\frac{1}{10}$ .

Report an Error

Example Question #11 : Exponents And Rational Numbers

Solve for .

$1024^x=\frac{1}{2}$

Possible Answers:

$\frac{1}{10}$

$-\frac{1}{10}$

Correct answer:

$-\frac{1}{10}$

Explanation:

$1024^x=(2^{10})^x$

We still don't have the same base however: $2=\frac{1}{2}^{-1}$

Then,

$1024^x=(2^{10})^x=\left[\left(\frac{1}{2}\right)^{-1}\right]^{10x}$ .

With same base we can set up an equation of -10x=1 .

Divide both sides by and we get $x=\frac{-1}{10}$ .

Report an Error

Example Question #31 : Exponents

Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.

Quantity A Quantity B

4³3⁴

Possible Answers:

The two quantities are equal.

Quantity A is greater.

The answer cannot be determined from the information given.

Quantity B is greater.

Correct answer:

Quantity B is greater.

Explanation:

In order to determine the relationship between the quantities, solve each quantity.

4³is 4 * 4 * 4 = 64

3⁴ is 3 * 3 * 3 * 3 = 81

Therefore, Quantity B is greater.

Report an Error

Example Question #32 : Exponents

Quantity A: $(-1)^{137}$

Quantity B:

Possible Answers:

The relationship cannot be determined from the information given.

Quantity A is greater.

The two quantities are equal.

Quantity B is greater.

Correct answer:

Quantity B is greater.

Explanation:

(–1) ¹³⁷= –1

–1 < 0

(–1) ^{odd #} always equals –1.

(–1) ^{even #} always equals +1.

Report an Error

Example Question #34 : Algebra

$2^{-5}$

Possible Answers:

$-\frac{1}{32}$

$\frac{1}{32}$

Correct answer:

$\frac{1}{32}$

Explanation:

Anything raised to negative power means over the base raised to the postive exponent.

$2^{-5}=\frac{1}{2^5}=\frac{1}{32}$

Report an Error

Example Question #38 : Algebra

Which of the following is not the same as the others?

Possible Answers:

$(\frac{1}{2})^{^{-24}}$

$4^{12}$

64^4

16^8

$2^{24}$

Correct answer:

16^8

Explanation:

Let's all convert the bases to .

$4^{12}=[2^2]^{12}=2^{24}$

$64^4=(2^6)^4=2^{24}$

$16^8=[2^4]^8=2^{32}$

$\left(\frac{1}{2}\right)^{^{-24}}$ This one may be intimidating but $2=\frac{1}{2}^{-1}$ .

Therefore,

$\left(\left[\frac{1}{2}\right]^{-24}\right)^{-1}=2^{24}$

$2^{24}$

16^8 is not like the answers so this is the correct answer.

Report an Error

All GRE Math Resources

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

Popular Subjects

Spanish Tutors in San Francisco-Bay Area, LSAT Tutors in Chicago, GMAT Tutors in Denver, Statistics Tutors in Atlanta, Physics Tutors in Los Angeles, English Tutors in Los Angeles, Computer Science Tutors in Miami, Computer Science Tutors in Washington DC, Computer Science Tutors in Philadelphia, Biology Tutors in Washington DC

Popular Courses & Classes

ACT Courses & Classes in Miami, SAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Washington DC, MCAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Boston, SSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Phoenix, ISEE Courses & Classes in Phoenix, ISEE Courses & Classes in Los Angeles, SSAT Courses & Classes in Seattle

Popular Test Prep

GMAT Test Prep in Denver, SAT Test Prep in Philadelphia, ISEE Test Prep in Phoenix, SSAT Test Prep in Philadelphia, ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in Denver, MCAT Test Prep in Philadelphia, GMAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Miami, ISEE Test Prep in New York City

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 : Exponents

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #3 : Exponents And Rational Numbers

Example Question #2 : Exponents And Rational Numbers

Example Question #8 : Exponents And Rational Numbers

Example Question #9 : Exponents And Rational Numbers

Example Question #10 : Exponents And Rational Numbers

Example Question #11 : Exponents And Rational Numbers

Example Question #31 : Exponents

Example Question #32 : Exponents

Example Question #34 : Algebra

Example Question #38 : Algebra

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details