Last visit was: 25 Apr 2026, 04:07 It is currently 25 Apr 2026, 04:07
Home
Messages
Tests
Schools
Events
Close
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.

Customized
for You

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

Track
Your Progress

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

Practice
Pays

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
GMATMadeeasy
User avatar
Joined: 25 Dec 2009
Last visit: 17 Nov 2011
Posts: 65
Own Kudos:
1,915
 [1]
Given Kudos: 3
Posts: 65
Kudos: 1,915
 [1]
Power expression and modulus - GMAT standard approach 23 Jan 2010, 11:12
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Question : \(a^b^c\)

How one will interpret this ?\((a^b)^c\) or \((a)^(b^c)\)

Second :
\((81)^1/4\) ; It is equivalent to 3 and or -3 in GMAT ? I am aware that \(\sqrt{(x^2)}\) is always positive value.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
andrewcs
User avatar
Joined: 21 Jan 2010
Last visit: 17 May 2010
Posts: 40
Own Kudos:
61
Location: Canada
Concentration: General
Posts: 40
Kudos: 61
Power expression and modulus - GMAT standard approach 23 Jan 2010, 12:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATMadeeasy
Question : \(a^b^c\)

How one will interpret this ?\((a^b)^c\) or \((a)^(b^c)\)

Second :
\((81)^1/4\) ; It is equivalent to 3 and or -3 in GMAT ? I am aware that \(\sqrt{(x^2)}\) is always positive value.
Show more

You would interpret \(a^b^c\) as \(a^(b^c)\) - the rule is to work 'top-down'. To me, it would feel 'funny' to evaluation a^b before evaluation b^c.

The second one confuses me:
\(\sqrt{(x^2)}\) is x always positive?
Take \(x=-2\) for example:
\((-2)^2= 4\)
\(\sqrt{4}=+2, -2\), so x could have been either positive or negative.

Hence, \((81)^1/4\) is +3 or -3, but you cannot tell from the equation.
User avatar
GMATMadeeasy
User avatar
Joined: 25 Dec 2009
Last visit: 17 Nov 2011
Posts: 65
Own Kudos:
1,915
Given Kudos: 3
Posts: 65
Kudos: 1,915
Power expression and modulus - GMAT standard approach 23 Jan 2010, 12:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
andrewcs
GMATMadeeasy
Question : \(a^b^c\)

How one will interpret this ?\((a^b)^c\) or \((a)^(b^c)\)

Second :
\((81)^1/4\) ; It is equivalent to 3 and or -3 in GMAT ? I am aware that \(\sqrt{(x^2)}\) is always positive value.

You would interpret \(a^b^c\) as \(a^(b^c)\) - the rule is to work 'top-down'. To me, it would feel 'funny' to evaluation a^b before evaluation b^c.

The second one confuses me:
\(\sqrt{(x^2)}\) is x always positive?
Take \(x=-2\) for example:
\((-2)^2= 4\)
\(\sqrt{4}=+2, -2\), so x could have been either positive or negative.

Hence, \((81)^1/4\) is +3 or -3, but you cannot tell from the equation.
Show more

I concur with both the points you mentioned. However, for first point , that is top down approach of exponent, I will post a good question in a while to solve. For second point, refer to GMAt Official guide , maths theory section ,it explicitly indicates that \(\sqrt{x^2}=|x|\) . I extended the definition further from x^2 to x^4.

I do not know what is the final answer .
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,141
 [2]
Given Kudos: 105,878
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,822
Kudos: 811,141
 [2]
Power expression and modulus - GMAT standard approach 24 Jan 2010, 01:15
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATMadeeasy
Question : \(a^b^c\)

How one will interpret this ?\((a^b)^c\) or \((a)^(b^c)\)

Second :
\((81)^1/4\) ; It is equivalent to 3 and or -3 in GMAT ? I am aware that \(\sqrt{(x^2)}\) is always positive value.
Show more

First question: \(a^m^n=a^{(m^n)}\) and not \((a^m)^n\), for instance \(3^{3^3}=3^{(3^3)}=3^{27}\).

Second question: \(\sqrt[_{even}]{x}\geq0\) - Even roots have only a positive value on the GMAT. (well if x=0 then it will obviously be 0). So \(\sqrt[4]{81}=3\), not +3 and -3.

Also general rule: \(\sqrt{x^2}=|x|\).

When we see the equation of a type: \(y=\sqrt{x^2}\) then \(y=|x|\), which means that \(y\) can not be negative but \(x\) can.

\(y\)can not be negative as \(y=\sqrt{some expression}\), and even root from the expression (some value) is never negative (as for GMAT we are dealing only with real numbers).

When the GMAT provides the square root sign for an even root, such as a square root, then the only accepted answer is the positive root.

That is, \(\sqrt{16} = 4\), NOT +4 or -4. In contrast, the equation \(x^2 = 16\) has TWO solutions, \(x=+4\)and \(x=-4.\)

On the other hand odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{64}=4\) and \(\sqrt[3]{-27}=-3\).

Hope it's clear.
User avatar
GMATMadeeasy
User avatar
Joined: 25 Dec 2009
Last visit: 17 Nov 2011
Posts: 65
Own Kudos:
1,915
 [1]
Given Kudos: 3
Posts: 65
Kudos: 1,915
 [1]
Power expression and modulus - GMAT standard approach 26 Jan 2010, 11:12
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let's try to solve this based on above.

What is the value of x ?

1 \sqrt{x^4} = 9
2 The average of x^2,6x and 3 is -2


P.S. First atement is square root of (x^4)
User avatar
andrewcs
User avatar
Joined: 21 Jan 2010
Last visit: 17 May 2010
Posts: 40
Own Kudos:
61
Location: Canada
Concentration: General
Posts: 40
Kudos: 61
Power expression and modulus - GMAT standard approach 26 Jan 2010, 11:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATMadeeasy
Let's try to solve this based on above.

What is the value of x ?

1 \sqrt{x^4} = 9
2 The average of x^2,6x and 3 is -2


P.S. First atement is square root of (x^4)
Show more

(1) I would think this gives x=+3 or x=-3 as possible solutions, so not sufficient.
(2) (x^2 + 6x + 3)/3 =-2
x^2 + 6x +3 = -6
x^2 + 6x + 9 = 0
x=-3

So (2) alone, B?
User avatar
DestinyChild
User avatar
Joined: 02 Oct 2009
Last visit: 23 Apr 2010
Posts: 124
Own Kudos:
82
Given Kudos: 4
Posts: 124
Kudos: 82
Power expression and modulus - GMAT standard approach 30 Jan 2010, 16:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
B;

agree with andrewcs... A doesnt give unique value, B does...
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,976
Own Kudos:
1,117
Posts: 38,976
Kudos: 1,117
Power expression and modulus - GMAT standard approach 29 Jan 2018, 00:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!