GMAT Math : Understanding exponents

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Understanding Exponents

$\frac{6^{3}}{36} + \frac{3^{68}}{3^{67}}=$

Possible Answers:

$\dpi{100} \small 36$

$\dpi{100} \small 9$

$\dpi{100} \small 18$

$\dpi{100} \small 6$

cannot be determined

Correct answer:

$\dpi{100} \small 9$

Explanation:

$\frac{6^{3}}{36} = \frac{6^{3}}{6^{2}} = 6$

$\frac{3^{68}}{3^{67}} = 3^{68-67} = 3$

Putting these together,

$\frac{6^{3}}{36} + \frac{3^{68}}{3^{67}}= 6 + 3 = 9$

Report an Error

Example Question #2 : Understanding Exponents

$\dpi{100} \small 3x^{4}\times x^{2}+x^{2}-x =$

Possible Answers:

$x(3x^{5}-x+1)$

$x(3x^{5}+x-1)$

$3x^{5}+x-1$

$3x^{7}$

$3x^{9}$

Correct answer:

$x(3x^{5}+x-1)$

Explanation:

$\dpi{100} \small 3x^{4}\times x^{2} =3x^{6}$

Then, $\dpi{100} \small 3x^{4}\times x^{2}+x^{2}-x = 3x^{6}+x^{2}-x = x(3x^{5}+x-1)$

Report an Error

Example Question #1 : Understanding Exponents

$4^{\frac{3}{2}} + 27^{\frac{2}{3}} =$

Possible Answers:

$\dpi{100} \small 27$

$\dpi{100} \small 16$

$\dpi{100} \small 8$

$\dpi{100} \small 17$

$\dpi{100} \small 9$

Correct answer:

$\dpi{100} \small 17$

Explanation:

$4^{\frac{3}{2}}=(4^{\frac{1}{2}})^{3} = 2^{3} = 8$

$27^{\frac{2}{3}}=(27^{\frac{1}{3}})^{2} = 3^{2} = 9$

Then putting them together, $4^{\frac{3}{2}} + 27^{\frac{2}{3}} = 8 + 9 = 17$

Report an Error

Example Question #3 : Understanding Exponents

Which of the following expressions is equivalent to this expression?

$\small \frac{x^{-\frac{1}{2}}}{x^{\frac{1}{3}}}$

You may assume that $\small x > 0$ .

Possible Answers:

$\small \small \small \frac{\sqrt[5]{x^{6}}}{x}$

$\small \frac{\sqrt[6]{x}}{x}$

$\small x\sqrt{x}$

$\small \sqrt[3]{x^{2}}$

$\small \small \frac{\sqrt[6]{x^{5}}}{x}$

Correct answer:

$\small \frac{\sqrt[6]{x}}{x}$

Explanation:

$\small \small \small \small \small \small \small \small \small \frac{x^{-\frac{1}{2}}}{x^{\frac{1}{3}}} = x^{-\frac{1}{2} -{\frac{1}{3}} } = x^{-\frac{2}{6} -{\frac{3}{6}} }= x^{-\frac{5}{6} }= \frac{1}{ x^{\frac{5}{6}}}$

$\small \small \small = \frac{1}{\sqrt[6]{x^{5}}}= \frac{\sqrt[6]{x}}{\sqrt[6]{x^{5}}\cdot \sqrt[6]{x}}= \frac{\sqrt[6]{x}}{x}$

Report an Error

Example Question #4 : Exponents

Simplify the following expression without a calculator:

$(\frac{9x^\frac{-5}{2}y^\frac{7}{4}}{x^\frac{3}{2}y^\frac{-1}{4}})^\frac{3}{2}$

Possible Answers:

$\frac{9y^3}{x^6}$

$27x^\frac{-3}{2}y^\frac{9}{4}$

$\frac{27y^3}{x^6}$

$\frac{27y^3}{x^3}$

$9x^\frac{-3}{2}y^\frac{9}{4}$

Correct answer:

$\frac{27y^3}{x^6}$

Explanation:

The easiest way to simplify is to work from the inside out. We should first get rid of the negatives in the exponents. Remember that variables with negative exponents are equal to the inverse of the expression with the opposite sign. For example, $a^\frac{-5}{2} = \frac{1}{a^\frac{5}{2}}$ So using this, we simplify: $(\frac{9x^\frac{-5}{2}y^\frac{7}{4}}{x^\frac{3}{2}y^\frac{-1}{4}})^\frac{3}{2} = (\frac{9(y^\frac{7}{4})(y^\frac{1}{4})}{(x^\frac{5}{2})(x^\frac{3}{2})})^\frac{3}{2}$

Now when we multiply variables with exponents, to combine them, we add the exponents together. For example, $(a^2)(a^2)=a^{2+2} = a^4$

Doing this to our expression we get it simplified to $(\frac{9y^2}{x^4})^\frac{3}{2}$ .

The next step is taking the inside expression and exponentiating it. When taking an exponent of a variable with an exponent, we actually multiply the exponents. For example, $(a^2)^4 = a^{(2*4)}= a^8$ . The other rule we must know that is an exponent of one half is the same as taking the square root. So for the $9^{3/2}=(\sqrt9)^3$ So using these rules, $(\frac{9y^2}{x^4})^\frac{3}{2} = \frac{9^{3/2}(y^2)^{3/2}}{(x^4)^{3/2}} = \frac{(\sqrt9)^3y^{(2*3/2)}}{x^{(4*3/2)}} = \frac{3^3y^3}{x^6}= \frac{27y^3}{x^6}$

Report an Error

Example Question #3 : Exponents

Rewrite as a single logarithmic expression:

$3 + \log_{3} x - 2\log_{3} y$

Possible Answers:

$\log_{3} \frac{3x}{y^{2}}$

$\log_{3} (3 + x -2y )$

$\log_{3} \frac{3x}{2y}$

$\log_{3} \frac{27x}{2y}$

$\log_{3} \frac{27x}{y^{2}}$

Correct answer:

$\log_{3} \frac{27x}{y^{2}}$

Explanation:

First, write each expression as a base 3 logarithm:

$3 = \log_{3}27$ since $3^{3} = 27$

$2 \log_{3}y = \log_{3} y^{2}$

Rewrite the expression accordingly, and apply the logarithm sum and difference rules:

$3 + \log_{3} x - 2\log_{3} y$

$=\log_{3}27 + \log_{3} x - \log_{3} y^{2}$

$=\log_{3}\left (27 \cdot x \right )- \log_{3} y^{2}$

$=\log_{3}\left (27 \cdot x \right \div y^{2} ) = \log_{3}\left (\frac{27 x }{y^{2}}\right )$

Report an Error

Example Question #7 : Exponents

If 3^p+3^p+3^p=3^q , what is in terms of ?

Possible Answers:

q-1

$\frac{q}{3}$

$\frac{q}{6}$

q+1

Correct answer:

q-1

Explanation:

We have $3^p+3^p+3^p=3*3^p=3^{p+1}=3^q$ .

So p+1=q , and p=q-1 .

Report an Error

Example Question #5 : Exponents

What are the last two digits, in order, of $6 ^{789}$ ?

Possible Answers:

Correct answer:

Explanation:

Inspect the first few powers of 6; a pattern emerges.

$6^{1} = 6$

$6^{2} = 36$

$6^{3} = 216$

$6^{4} = 1,296$

$6^{5} = 7,776$

$6^{6} = 46,656$

$6^{7} = 279,936$

$6^{8} = 1,679,616$

$6^ { 9 } =10,077,696$

$6^ { 10} =60,466,176$

As you can see, the last two digits repeat in a cycle of 5.

789 divided by 5 yields a remainder of 4; the pattern that becomes apparent in the above list is that if the exponent divided by 5 yields a remainder of 4, then the power ends in the diigts 96.

Report an Error

Example Question #32 : Algebra

Which of the following expressions is equal to the expression

$\left ( x^{3}\right ) ^{4} \cdot \left ( x^{3}\right ) ^{5}$ ?

Possible Answers:

$x^{60}$

$x^{15}$

$x^{180}$

$x^{12}$

$x^{27}$

Correct answer:

$x^{27}$

Explanation:

Use the properties of exponents as follows:

$\left ( x^{3}\right ) ^{4} \cdot \left ( x^{3}\right ) ^{5}$

$=x^{3\; \cdot \; 4} \cdot x^{3\; \cdot \; 5}$

$=x^{12} \cdot x^{15}$

$=x^{12+15}$

$=x^{27}$

Report an Error

Example Question #1 : Understanding Exponents

Simplify:

$\left [ \left ( x ^{5} \right )^{4} \right ]^{3}$

Possible Answers:

12x

$x ^{60}$

$x ^{12}$

60x

$60x ^{12}$

Correct answer:

$x ^{60}$

Explanation:

Apply the power of a power principle twice by multiplying exponents:

$\left [ \left ( x ^{5} \right )^{4} \right ]^{3} = \left ( x ^{5 \cdot 4} \right ) ^{3} = \left ( x ^{20} \right ) ^{3} = x ^{20 \cdot 3} = x ^{60 }$

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Atlanta, GMAT Tutors in Dallas Fort Worth, SSAT Tutors in Seattle, ISEE Tutors in Seattle, Algebra Tutors in New York City, SSAT Tutors in Chicago, French Tutors in Seattle, Physics Tutors in Los Angeles, Algebra Tutors in Dallas Fort Worth, GRE Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in Denver, LSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Washington DC, ACT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in New York City, GRE Courses & Classes in Atlanta, SAT Courses & Classes in Miami, ISEE Courses & Classes in Boston, LSAT Courses & Classes in Houston, ISEE Courses & Classes in Miami

Popular Test Prep

ACT Test Prep in Denver, ISEE Test Prep in Boston, GRE Test Prep in Atlanta, GMAT Test Prep in Washington DC, ISEE Test Prep in Phoenix, MCAT Test Prep in Boston, ISEE Test Prep in San Diego, GRE Test Prep in Miami, SAT Test Prep in Seattle, ACT 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:

GMAT Math : Understanding exponents

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Understanding Exponents

Example Question #2 : Understanding Exponents

Example Question #1 : Understanding Exponents

Example Question #3 : Understanding Exponents

Example Question #4 : Exponents

Example Question #3 : Exponents

Example Question #7 : Exponents

Example Question #5 : Exponents

Example Question #32 : Algebra

Example Question #1 : Understanding Exponents

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details