Last visit was: 21 Apr 2026, 14:26 It is currently 21 Apr 2026, 14:26
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
Back to Forum
Create Topic
655-705 (Hard)|   Exponents|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 Apr 2026
Posts: 109,728
Own Kudos:
810,464
 [33]
Given Kudos: 105,800
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: 109,728
Kudos: 810,464
 [33]
If a is a positive integer, which of the following is equal to (-4^a)^ 10 Feb 2023, 14:50
1
Kudos
Add Kudos
32
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

60% (02:00) correct 40% (02:18) wrong based on 513 sessions

History

Date
Time
Result
Not Attempted Yet
If a is a positive integer, which of the following is equal to \((-4^a)^{-4} + (-2^4)^{-2a}\) ?

A. \(-2^{-8a + 1}\)

B. \(-2^{-16a + 1}\)

C. \(2\)

D. \(2^{-8a + 1}\)

E. \(2^{-16a + 1}\)
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
gmatophobia
User avatar
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 19 Apr 2026
Posts: 3,173
Own Kudos:
11,439
 [5]
Given Kudos: 1,862
Location: India
Concentration: Strategy, Leadership
Posts: 3,173
Kudos: 11,439
 [5]
If a is a positive integer, which of the following is equal to (-4^a)^ 11 Feb 2023, 23:15
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If a is a positive integer, which of the following is equal to \((-4^a)^{-4} + (-2^4)^{-2a}\) ?

A. \(-2^{-8a + 1}\)

B. \(-2^{-16a + 1}\)

C. \(2\)

D. \(2^{-8a + 1}\)

E. \(2^{-16a + 1}\)
Show more

\((-4^a)^{-4} + (-2^4)^{-2a}\)

\((-1)^{-4}(4^a)^{-4} + (-1)^{-2a}(2^4)^{-2a}\)

\((2^{2a})^{-4} + (2^4)^{-2a}\)

\(2* 2^{-8a}\)

\(2^{-8a + 1}\)

Option D
General Discussion
User avatar
Akriti_Khetawat
User avatar
Joined: 21 Jul 2023
Last visit: 03 Oct 2025
Posts: 18
Own Kudos:
3
 [1]
Given Kudos: 14
Posts: 18
Kudos: 3
 [1]
If a is a positive integer, which of the following is equal to (-4^a)^ 06 Dec 2024, 23:49
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatophobia
Bunuel
If a is a positive integer, which of the following is equal to \((-4^a)^{-4} + (-2^4)^{-2a}\) ?

A. \(-2^{-8a + 1}\)

B. \(-2^{-16a + 1}\)

C. \(2\)

D. \(2^{-8a + 1}\)

E. \(2^{-16a + 1}\)

\((-4^a)^{-4} + (-2^4)^{-2a}\)

\((-1)^{-4}(4^a)^{-4} + (-1)^{-2a}(2^4)^{-2a}\)

\((2^{2a})^{-4} + (2^4)^{-2a}\)

\(2* 2^{-8a}\)

\(2^{-8a + 1}\)

Option D
Show more
Hi what happens to the -1 in this solution? Do they get cancelled?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 Apr 2026
Posts: 109,728
Own Kudos:
810,464
 [2]
Given Kudos: 105,800
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: 109,728
Kudos: 810,464
 [2]
If a is a positive integer, which of the following is equal to (-4^a)^ 07 Dec 2024, 00:55
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Akriti_Khetawat
gmatophobia
Bunuel
If a is a positive integer, which of the following is equal to \((-4^a)^{-4} + (-2^4)^{-2a}\) ?

A. \(-2^{-8a + 1}\)

B. \(-2^{-16a + 1}\)

C. \(2\)

D. \(2^{-8a + 1}\)

E. \(2^{-16a + 1}\)

\((-4^a)^{-4} + (-2^4)^{-2a}\)

\((-1)^{-4}(4^a)^{-4} + (-1)^{-2a}(2^4)^{-2a}\)

\((2^{2a})^{-4} + (2^4)^{-2a}\)

\(2* 2^{-8a}\)

\(2^{-8a + 1}\)

Option D
Hi what happens to the -1 in this solution? Do they get cancelled?
Show more

When raised to any nonzero even power, (-1) becomes 1. So, \( (-1)^{-4}=1 \) and \( (-1)^{-2a} =1\). Since these terms evaluate to 1, they are simply dropped from the equation.
User avatar
saynchalk
User avatar
Joined: 17 Sep 2023
Last visit: 26 Dec 2025
Posts: 195
Own Kudos:
258
Given Kudos: 847
Status:Always questioning myself
Location: India
Concentration: General Management, International Business
Schools: CBS
GMAT Focus 1: 525 Q74 V82 DI72
GPA: 3.1
WE:Sales (Computer Software)
Schools: CBS
GMAT Focus 1: 525 Q74 V82 DI72
Posts: 195
Kudos: 258
If a is a positive integer, which of the following is equal to (-4^a)^ 07 Dec 2024, 01:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Akriti_Khetawat
gmatophobia
Bunuel
If a is a positive integer, which of the following is equal to \((-4^a)^{-4} + (-2^4)^{-2a}\) ?

A. \(-2^{-8a + 1}\)

B. \(-2^{-16a + 1}\)

C. \(2\)

D. \(2^{-8a + 1}\)

E. \(2^{-16a + 1}\)

\((-4^a)^{-4} + (-2^4)^{-2a}\)

\((-1)^{-4}(4^a)^{-4} + (-1)^{-2a}(2^4)^{-2a}\)

\((2^{2a})^{-4} + (2^4)^{-2a}\)

\(2* 2^{-8a}\)

\(2^{-8a + 1}\)

Option D
Hi what happens to the -1 in this solution? Do they get cancelled?
Show more


I think what happens is that (-1)^2n [ -1 RAISED TO ANY EVEN NUMBER] will always be positive so they become +1 which is where they disappear after multiplication
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,955
Own Kudos:
1,117
Posts: 38,955
Kudos: 1,117
If a is a positive integer, which of the following is equal to (-4^a)^ 27 Jan 2026, 13:37
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.
Moderators:
Bunuel
Math Expert
109728 posts
Krunaal
Tuck School Moderator
853 posts