Find all School-related info fast with the new School-Specific MBA Forum

It is currently 29 Nov 2015, 16:59
GMAT Club Tests


GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

for You

we will pick new questions that match your level based on your Timer History

Your Progress

every week, we’ll send you an estimated GMAT score based on your performance


we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Exponents and Roots on the GMAT: Tips and hints

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 30410
Followers: 5095

Kudos [?]: 57469 [1] , given: 8814

Exponents and Roots on the GMAT: Tips and hints [#permalink] New post 24 Jul 2014, 06:33
This post received
Expert's post
This post was

Exponents and Roots: Tips and hints

This post is a part of the Quant Tips and Hints by Topic Directory focusing on Quant topics and providing examples of how to approach them. Most of the questions are above average difficulty.


Exponents are a "shortcut" method of showing a number that was multiplied by itself several times. For instance, number \(a\) multiplied \(n\) times can be written as \(a^n\), where \(a\) represents the base, the number that is multiplied by itself \(n\) times and \(n\) represents the exponent. The exponent indicates how many times to multiple the base, \(a\), by itself.


1. Exponents one and zero:
\(a^0=1\) Any nonzero number to the power of 0 is 1.
For example: \(5^0=1\) and \((-3)^0=1\)
• Note: the case of 0^0 is not tested on the GMAT.

\(a^1=a\) Any number to the power 1 is itself.

2. Powers of zero:
If the exponent is positive, the power of zero is zero: \(0^n = 0\), where \(n > 0\).

If the exponent is negative, the power of zero (\(0^n\), where \(n < 0\)) is undefined, because division by zero is implied.

3. Powers of one:
\(1^n=1\) The integer powers of one are one.

4. Negative powers:
Important: you cannot rise 0 to a negative power because you get division by 0, which is NOT allowed. For example, \(0^{-1} = \frac{1}{0}=undefined\).

5. Powers of minus one:
If n is an even integer, then \((-1)^n=1\).

If n is an odd integer, then \((-1)^n =-1\).

6. Operations involving the same exponents:
Keep the exponent, multiply or divide the bases



\(a^m^n=a^{(m^n)}\) and not \((a^m)^n\) (if exponentiation is indicated by stacked symbols, the rule is to work from the top down)

7. Operations involving the same bases:
Keep the base, add or subtract the exponent (add for multiplication, subtract for division)


8. Fraction as power:



Roots (or radicals) are the "opposite" operation of applying exponents. For instance x^2=16 and square root of 16=4.


General rules:
1. \(\sqrt{x}\sqrt{y}=\sqrt{xy}\) and \(\frac{\sqrt{x}}{\sqrt{y}}=\sqrt{\frac{x}{y}}\).

2. \((\sqrt{x})^n=\sqrt{x^n}\)

3. \(x^{\frac{1}{n}}=\sqrt[n]{x}\)

4. \(x^{\frac{n}{m}}=\sqrt[m]{x^n}\)

5. \({\sqrt{a}}+{\sqrt{b}}\neq{\sqrt{a+b}}\)

6. \(\sqrt{x^2}=|x|\), when \(x\leq{0}\), then \(\sqrt{x^2}=-x\) and when \(x\geq{0}\), then \(\sqrt{x^2}=x\).

7. When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

8. Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

This week's PS question
This week's DS Question

Theory: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

All DS roots problems to practice: search.php?search_id=tag&tag_id=49
All PS roots problems to practice: search.php?search_id=tag&tag_id=113

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Please share your Exponents and Roots tips below and get kudos point. Thank you.


PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
1 KUDOS received
Joined: 27 Aug 2014
Posts: 30
GMAT Date: 09-27-2014
Followers: 1

Kudos [?]: 6 [1] , given: 25

GMAT ToolKit User
Re: Exponents and Roots on the GMAT: Tips and hints [#permalink] New post 27 Aug 2014, 05:10
This post received
This post was
3^n will always have an even number of tens.

Example: 27, 81, 729, etc
Re: Exponents and Roots on the GMAT: Tips and hints   [#permalink] 27 Aug 2014, 05:10
    Similar topics Author Replies Last post
8 Algebra: Tips and hints Bunuel 2 16 Jul 2014, 10:30
22 Experts publish their posts in the topic Absolute Value: Tips and hints Bunuel 6 09 Jul 2014, 06:04
31 Experts publish their posts in the topic Inequalities: Tips and hints Bunuel 1 02 Jul 2014, 03:33
8 Remainders: Tips and hints Bunuel 1 23 Jun 2014, 02:33
45 Number Properties: Tips and hints Bunuel 8 04 Jun 2014, 11:25
Display posts from previous: Sort by

Exponents and Roots on the GMAT: Tips and hints

  Question banks Downloads My Bookmarks Reviews Important topics  

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.