GRE Math : How to add 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 #4 : How To Add Exponents

Simplify: y³x⁴(yx³ + y²x² + y¹⁵ + x²²)

Possible Answers:

2x⁴y⁴ + 7y¹⁵ + 7x²²

y⁴x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

y³x¹² + y⁶x⁸ + y⁴⁵ + x⁸⁸

y³x¹² + y¹²x⁸ + y²⁴x⁴ + y³x²³

y³x¹² + y⁶x⁸ + y⁴⁵x⁴ + y³x⁸⁸

Correct answer:

y⁴x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

Explanation:

When you multiply exponents, you add the common bases:

y⁴ x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

Report an Error

Example Question #1 : Exponential Operations

Indicate whether Quantity A or Quantity B is greater, or if they are equal, or if there is not enough information given to determine the relationship.

$\dpi{100} \small n>0$

Quantity A: $\dpi{100} \small 16^{n+2}$

Quantity B: $\dpi{100} \small 2^{4}\times (8^{n+1})^{2}\div 4^{n}$

Possible Answers:

Quantity B is greater.

The relationship cannot be determined from the information given.

The quantities are equal.

Quantity A is greater.

Correct answer:

Quantity B is greater.

Explanation:

By using exponent rules, we can simplify Quantity B.

$\dpi{100} \small \dpi{100} \small 2^{4}\times (8^{2n+2})\div 4^{n}$

$\dpi{100} \small \dpi{100} \small 2^{4}\times 2^{3(2n+2)}\div 4^{n}$

$\dpi{100} \small \dpi{100} \small 2^{4}\times 2^{6n+6}\div 4^{n}$

$\dpi{100} \small \dpi{100} \small 2^{6n+10}\div 4^{n}$

$\dpi{100} \small \dpi{100} \small 2^{6n+10}\div 2^{2n}$

$\dpi{100} \small 2^{4n+10}$

Also, we can simplify Quantity A.

$\dpi{100} \small =2^{4(n+2)}$

$\dpi{100} \small =2^{4n+8}$

Since n is positive, $\dpi{100} \small 4n+10>4n+8$

Report an Error

Example Question #6 : Exponential Operations

If $\frac{3^{y - 1}}{3^{-2}} = 27^{y}3^{y}$ , what is the value of ?

Possible Answers:

$\frac{2}{3}$

$\frac{3}{2}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

Rewrite the term on the left as a product. Remember that negative exponents shift their position in a fraction (denominator to numerator).

$3^{y-1}*3^2=27^y3^y$

The term on the right can be rewritten, as 27 is equal to 3 to the third power.

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

Exponent rules dictate that multiplying terms allows us to add their exponents, while one term raised to another allows us to multiply exponents.

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

$3^{y+1}=3^{3y+y}=3^{4y}$

We now know that the exponents must be equal, and can solve for .

y+1=4y

1=3y

$\frac{1}{3}=y$

Report an Error

Example Question #11 : Exponential Operations

If $5^2 \times 5^n = 5^{12}$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Since the base is 5 for each term, we can say 2 + n =12. Solve the equation for n by subtracting 2 from both sides to get n = 10.

Report an Error

Example Question #12 : Exponential Operations

Simplify $x^{3}x^{6} + (x^{3})^{3} + x^{3}x^{2}x^{2}x^{2}$ .

Possible Answers:

$x^{27} + x^{18} + x^{9}$

$3x^{3}$

$2x^{9} + x^{27}$

$x^{18} + 2x^{9}$

$3x^{9}$

Correct answer:

$3x^{9}$

Explanation:

Start by simplifying each individual term between the plus signs. We can add the exponents in x^3x^6 and x^3x^2x^2x^2 so each of those terms becomes x^9 . Then multiply the exponents in (x^3)^3 so that term also becomes x^9 . Thus, we have simplified the expression to x^9 + x^9 + x^9 which is $3x^{9}$ .

Report an Error

Example Question #1551 : Gre Quantitative Reasoning

Simplify $x^{^{3}}x^{^{5}} - x^{^{2}} + (y^{^{2}})^{^{2}}$ .

Possible Answers:

$x^{15} - x^{2} + y^{4}$

$(xy)^{2}$

$x^{6}+y^{4}$

$x^{8} - x^{2} + y^{2}$

$x^{8} - x^{^{2}} + y^{4}$

Correct answer:

$x^{8} - x^{^{2}} + y^{4}$

Explanation:

First, simplify $x^{3}x^{5}$ by adding the exponents to get $x^{8}$ .

Then simplify $(y^{2})^{2}$ by multiplying the exponents to get $y^{4}$ .

This gives us $x^{8} - x^{^{2}} + y^{4}$ . We cannot simplify any further.

Report an Error

Example Question #14 : Exponential Operations

If $3^4 \cdot 3^8 = 9^x$ , what is the value of

Possible Answers:

$\frac{4}{3}$

$\frac{32}{9}$

Correct answer:

Explanation:

To attempt this problem, note that 3^2=(3)^2=9^1=9 .

Now note that when multiplying numbers, if the base is the same, we may add the exponents:

$3^4 \cdot 3^8 = 3^{4+8}=3^{12}$

This can in turn be written in terms of nine as follows (recall above)

$3^{12}=9^{\frac{12}{2}}=9^6$

9^6=9^x

x=6

Report an Error

Example Question #15 : Exponential Operations

If $(3^2\cdot3^5)^3=3^x$ , what is the value of

Possible Answers:

Correct answer:

Explanation:

When dealing with exponenents, when multiplying two like bases together, add their exponents:

$3^2\cdot3^5=3^7$

However, when an exponent appears outside of a parenthesis, or if the entire number itself is being raised by a power, multiply:

$(3^7)^3=3^{7\cdot 3}=3^{21}$

$3^{21}=3^{x}$

x=21

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 Diego, Chemistry Tutors in Phoenix, French Tutors in Atlanta, MCAT Tutors in Atlanta, Physics Tutors in Chicago, Chemistry Tutors in Los Angeles, MCAT Tutors in Los Angeles, Calculus Tutors in Chicago, GRE Tutors in Philadelphia, GRE Tutors in Los Angeles

Popular Courses & Classes

ACT Courses & Classes in New York City, SAT Courses & Classes in Boston, ACT Courses & Classes in Miami, MCAT Courses & Classes in Houston, SAT Courses & Classes in Washington DC, ISEE Courses & Classes in Miami, ACT Courses & Classes in Houston, LSAT Courses & Classes in New York City, GMAT Courses & Classes in Washington DC, SSAT Courses & Classes in Washington DC

Popular Test Prep

ISEE Test Prep in Philadelphia, MCAT Test Prep in Houston, ISEE Test Prep in Atlanta, LSAT Test Prep in Chicago, ACT Test Prep in New York City, ISEE Test Prep in Chicago, SSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Boston, GMAT Test Prep in San Diego, GMAT Test Prep in Dallas Fort Worth

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 : How to add exponents

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #4 : How To Add Exponents

Example Question #1 : Exponential Operations

Example Question #6 : Exponential Operations

Example Question #11 : Exponential Operations

Example Question #12 : Exponential Operations

Example Question #1551 : Gre Quantitative Reasoning

Example Question #14 : Exponential Operations

Example Question #15 : Exponential Operations

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details