GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 28Live Online Class with Top GRE Expert Mike Butville
08:00 PM EDT
-10:00 PM EDT
Top scores are possible when you enroll in a powerful GRE course, taught live online + 6 months access to TTP GRE OnDemand video courses included! Class starts Mon/Wed Sept. 28, 2026 - Dec. 9, 2026, 8:00pm-10:00pm EST
((2^4)^6)^8
[#permalink]
20 May 2020, 08:57
20 May 2020, 08:57
Expert Reply
00:00
Question Stats:
88% (00:39) correct
11% (00:47) wrong based on 109 sessions
Hide Show timer Statistics
Quantity A |
Quantity B |
\(((2^{4})^{6})^{8}\) |
\(((8^6)^4)^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: ((2^4)^6)^8
[#permalink]
20 May 2020, 08:57
20 May 2020, 08:57
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
((2^4)^6)^8
[#permalink]
21 May 2020, 05:26
21 May 2020, 05:26
1
Carcass wrote:
Quantity A |
Quantity B |
\(((2^{4})^{6})^{8}\) |
\(((8^6)^4)^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Key property: \((x^a)^b = x^{ab}\)
Extension of key property: \(((x^a)^b)^c = x^{abc}\)
Apply the properties to get:
QUANTITY A: \(((2^{4})^{6})^{8}=2^{192}\)
QUANTITY B: \(((8^6)^4)^2=8^{48}\)
In order to compare these values we need the same base.
Rewrite \(8\) as \(2^3\) to get:
QUANTITY A: \(2^{192}\)
QUANTITY B: \((2^3)^{48}\)
Simplify:
QUANTITY A: \(2^{192}\)
QUANTITY B: \(2^{144}\)
Answer: A
RELATED VIDEO
