GRE Math : Exponents and Rational Numbers

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 #21 : Gre Quantitative Reasoning

find x

8^x=2^x+6

Possible Answers:

-1

2 or -1

Correct answer:

Explanation:

8 = 2³

(2³)^x = 2^3x

2^3x = 2^x+6 <- when the bases are the same, you can set the exponents equal to each other and solve for x

3x=x+6

2x=6

x=3

Report an Error

Example Question #1 : How To Find An Exponent From A Rational Number

Compare $3^{6}$ and $27^{2}$ .

Possible Answers:

$3^{6} < 27^{2}$

$3^{6} > 27^{2}$

The relationship cannot be determined from the information given.

$3^{6} = 27^{2}$

Correct answer:

$3^{6} = 27^{2}$

Explanation:

First rewrite the two expressions so that they have the same base, and then compare their exponents.

$27 = 3^{3}$

$27^2 = (3^{3})^2$

Combine exponents by multiplying: $(3^{3})^2 = 3^6$

This is the same as the first given expression, so the two expressions are equal.

Report an Error

Example Question #3 : Exponents And Rational Numbers

Solve for .

2^x=32

Possible Answers:

Correct answer:

Explanation:

can be written as 2^5.

Since there is a common base of , we can say

2^x=2^5 or x=5 .

Report an Error

Example Question #1 : How To Find An Exponent From A Rational Number

Solve for .

$3^x=\frac{1}{9}$

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

Explanation:

The basees don't match.

However:

$\frac{1}{3}=3^{-1}$ thus we can rewrite the expression as $\frac{1}{9}=\left(\frac{1}{3}\right)^2$ .

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

So, $(3^{-1})^{2}$ $=3^{-2}$ . x=-2 .

Report an Error

Example Question #2 : How To Find An Exponent From A Rational Number

Solve for .

$\frac{1}{4}^x=256$

Possible Answers:

$\frac{1}{4}$

256

$-\frac{1}{4}$

Correct answer:

Explanation:

The bases don't match.

However:

$4=\frac{1}{4}^{-1}$ and we recognize that 256=4^4 .

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

$\left(\frac{1}{4}^{-1}\right)^4=\frac{1}{4}^{-4}$ .

x=-4

Report an Error

Example Question #3 : How To Find An Exponent From A Rational Number

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 #5 : How To Find An Exponent From A Rational Number

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 #6 : How To Find An Exponent From A Rational Number

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 #7 : How To Find An Exponent From A Rational Number

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 #8 : 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

All GRE Math Resources

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

Popular Subjects

Biology Tutors in Miami, GRE Tutors in Denver, Physics Tutors in Miami, Calculus Tutors in Dallas Fort Worth, Biology Tutors in Dallas Fort Worth, Physics Tutors in Dallas Fort Worth, LSAT Tutors in Los Angeles, SAT Tutors in Los Angeles, ISEE Tutors in Atlanta, ISEE Tutors in Chicago

Popular Courses & Classes

GMAT Courses & Classes in Houston, LSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in New York City, Spanish Courses & Classes in Miami, ISEE Courses & Classes in New York City, GRE Courses & Classes in Phoenix, GRE Courses & Classes in Chicago, SSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Boston, GMAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ISEE Test Prep in San Diego, SSAT Test Prep in Washington DC, SAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Los Angeles, SSAT Test Prep in Atlanta, ACT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Houston, ISEE Test Prep in Philadelphia, LSAT Test Prep in Miami

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 and Rational Numbers

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #21 : Gre Quantitative Reasoning

Example Question #1 : How To Find An Exponent From A Rational Number

Example Question #3 : Exponents And Rational Numbers

Example Question #1 : How To Find An Exponent From A Rational Number

Example Question #2 : How To Find An Exponent From A Rational Number

Example Question #3 : How To Find An Exponent From A Rational Number

Example Question #5 : How To Find An Exponent From A Rational Number

Example Question #6 : How To Find An Exponent From A Rational Number

Example Question #7 : How To Find An Exponent From A Rational Number

Example Question #8 : Exponents And Rational Numbers

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details