GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Oct 2019, 01:51

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.

Close

Request Expert Reply

Confirm Cancel

If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
B
Joined: 26 Mar 2017
Posts: 106
Re: If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to  [#permalink]

Show Tags

New post 22 Jun 2017, 10:03
Another approach:

(-2^n)^-2 = (2^-n)^2

(-1)^-2 * 2^-2n + 2^-2n

= 2^(-2n+1)
_________________
I hate long and complicated explanations!
Intern
Intern
avatar
B
Joined: 03 Nov 2016
Posts: 2
Re: If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to  [#permalink]

Show Tags

New post 23 Jul 2017, 19:57
Hello,

Could anybody help me? Why is this wrong:


\((-2^{n})^{-2}\) = \(((-2)^n)^{-2}\) = \(-2^{-2n}\)
\((2^{-n})^{2}\) = \(((2)^{-n})^{2}\) = \(2^{-2n}\)

\(-2^{-2n}\) + \(2^{-2n}\) = 0

The answer I got was 0. I can follow the steps to get to D, but I'm not seeing my mistake, which originally led me to A.

Thanks!
Intern
Intern
avatar
B
Joined: 10 Jul 2018
Posts: 13
Re: If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to  [#permalink]

Show Tags

New post 26 Sep 2018, 11:56
broall wrote:
lpetroski wrote:
If n is a positive integer, then \((-2^{n})^{-2}\) +\((2^{-n})^{2}\) =

A. 0

B. \(2^{(-2n)}\)

C. \(2^{(2n)}\)

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

E. \(2^{(2n+1)}\)


\((-2^n)^{-2}+(2^{-n})^2 \\
=\frac{1}{(-2^n)^2}+2^{-2n} \\
=\frac{1}{(-2)^{2n}}+\frac{1}{2^{2n}}\\
=\frac{1}{2^{2n}}+\frac{1}{2^{2n}}\\
=\frac{2}{2^{2n}}\\
=\frac{1}{2^{2n-1}} \\
=2^{-(2n-1)}\\
=2^{-2n+1}
\)

The answer is D.


Can someone explain how 2/2^2n become 1/2^(2n-1) please?

=\frac{2}{2^{2n}}\\
=\frac{1}{2^{2n-1}} \\
VP
VP
User avatar
D
Joined: 31 Oct 2013
Posts: 1467
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
CAT Tests
If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to  [#permalink]

Show Tags

New post 30 Sep 2018, 09:15
lpetroski wrote:
If n is a positive integer, then \((-2^{n})^{-2}\) +\((2^{-n})^{2}\) =

A. 0

B. \(2^{(-2n)}\)

C. \(2^{(2n)}\)

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

E. \(2^{(2n+1)}\)


*** negative base having positive even exponent is equal to positive base having even exponent. No difference. *****

\((-2^{n})^{-2}\) +\((2^{-n})^{2}\)

= \(2^{-2n} + 2^{-2n}\)

= \(2^{-2n} (1 + 1 )\)

= \(2^{-2n} * 2\)

= \(2^{-2n +1}\)

The best answer is D.
Senior Manager
Senior Manager
User avatar
P
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 434
Premium Member
Re: If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to  [#permalink]

Show Tags

New post 05 Jun 2019, 11:39
You can't factor out a common number if it's not the same base.

\((-2^{n})^{-2} + (2^{-n})^{2}\)

\((-1^{n}*2^{n})^{-2} + 2^{(-n*2)}\)

\((-1^{-2n}*2^{-2n}) + 2^{-2n}\)

\((\frac{1}{-1^{2n}}*2^{-2n}) + 2^{-2n}\)
Base 1 to the power of anything is 1 and even exponents remove negative...

\((\frac{1}{1}*2^{-2n}) + 2^{-2n}\)

\(2^{-2n} + 2^{-2n}\)

\(2^{-2n}(1+1)\)

\(2^{-2n}(2)\)

\(2^{-2n+1}\)
VP
VP
User avatar
P
Joined: 14 Feb 2017
Posts: 1213
Location: Australia
Concentration: Technology, Strategy
Schools: LBS '22
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
WE: Management Consulting (Consulting)
Reviews Badge CAT Tests
Re: If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to  [#permalink]

Show Tags

New post 10 Jul 2019, 16:51
Got this wrong on EP2, GMATPrep 6. It was question 16.

STUPID mistakes were made as I took the algebraic approach and incorrectly didn't apply the even power to the base properly.

The plug-in method is so much more effective on this.
_________________
Goal: Q49, V41

+1 Kudos if I have helped you
GMAT Club Bot
Re: If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to   [#permalink] 10 Jul 2019, 16:51

Go to page   Previous    1   2   [ 26 posts ] 

Display posts from previous: Sort by

If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne