If n is a positive integer, then ((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4

Question

GMATBusters’ Quant Quiz Question -8

For past quiz questions, click  here

If n is a positive integer, then  ((-3)^n)^{-4} + (3^{-n})^4 + ((-3)^{-n})^4 =

A  (\frac{1}{3})^{(-4n)}

B  (\frac{1}{3})^{(-4n+1)}

C  3^{(-4n+ 1)}

D  3^{(-4n)}

E  3^{(-4n -1)}

chetan2u · Answer

If n is a positive integer, then  ((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4 =

Now all are raised to even power 4, so we can take base as 3.
If n is a positive integer, then  ((-3)^n)^{-4} + (3^{-n})^4 + ((-3)^{-n})^4 =  If n is a positive integer, then  ((3)^n)^{-4} + (3^{-n})^4 + ((3)^{-n})^4 = 3*3^{-4n}=3^{-4n+1}

C

Raxit85 · Answer

n = positive integer
 ((-3)^n)^-4 + (3^-n)4 + ((-3)^-n)^4 =
(-3)^-4n + 3^-4n + (-3)^-4n ------------------------(A)
As (-3)^-4n = (-1/3)^4n 
 (-1/3)^4n + (1/3)^4n +(-1/3)^4n -------------------------------(B)
As n is a positive integer, 4n will always be even
So, (-1/3)^4n = (1/3)^4n
Applying this result in expression (B),
(1/3)^4n + (1/3)^4n + (1/3)^4n =
3 x (1/3)^4n
3 x 1/3^4n
3^1-4n, So 3^-4n + 1
 Imo. C

ashwini2k6jha · Answer

ANSWER:C
((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4 
=(-3)^-4n+(3)^-4n+(-3)^-4n
=1/(-3)^4n+1/(3)^4n+1/(-3)^4n
=3/(3)^4n=(3)^1-4n

uc26 · Answer

The easiest way is the test any positive integer for n say 2.
The equation then becomes  3/9^4= 1/3^7 
Test the same n=2 on the choices. Only choice C matches.

Answer: C

Archit3110 · Answer

GIVEN If n is a positive integer, then ((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4 =
which can re written as
(1/(-3)^n ) ^4 + (1/3^n)^4 + (1/(-3)^n) ^4
at n =1
(1/(-3))^4 + (1/3)^4 + (1/(-3)) ^4
1/81+1/81+1/81 ; 3/81 ; 1/27 ( target value ) 
check with given options , 
for option C 
3^(-4n+ 1) at n= 1
3^-3 ; 1/3^3 ; 1/27 same as our target value

OPTION C

If n is a positive integer, then ((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4 =
A (1/3)^(-4n) ; 
B (1/3)^(-4n+1) ; 
C 3^(-4n+ 1)
D 3^(-4n)
E 3^(-4n -1)

SohGMAT2020 · Answer

If n is a positive integer, then ((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4 =

A (1/3)^(-4n)
B (1/3)^(-4n+1)
C 3^(-4n+ 1)
D 3^(-4n)
E 3^(-4n -1)

Solution:

(-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4

= ((-3)^-4n + (3^-4n) + ((-3)^-4n

= ((-1)^-4n *(3)^-4n + (3^-4n) + ((-1)^-4n * (3)^-4n)

= (3)^-4n + (3^-4n) + (3)^-4n)

= 3*(3^-4n)

= (3^-4n+1)

So, option C is correct

yashikaaggarwal · Answer

Let N = 1
=>> {(-3)^n)^-4 + (3^-n)^4 + (-3)^-n)^4} 
=>> {(-3)^1)^-4 + (3^-1)^4 + (-3)^-1)^4} 
=>> {(-3)^-4 + (1/3)^4 + (1/-3)^4} 
=>> {(1/-3)^4 + (1/3)^4 + (1/-3)^4} 
=>> {1/81+1/81+1/81}
=>> {3/81} =>>> 1/27 = L.H.S

Putting value of N = 1 in options:

A (1/3)^(-4n)
=> 1/3^-4 
=> 3^4 => 81 (≠1/27)

B (1/3)^(-4n+1)
=> 1/3^(-4+1)
=> 1/3^(-3)
=> 3^3 => 27 (≠1/27)

C 3^(-4n+ 1)
=> 3^(-4+1)
=> 3^-3
=> 1/3^3 => 1/27 (=1/27)

D 3^(-4n)
=> 3^-4
=> 1/3^4
=> 1/81 (≠1/27)

E 3^(-4n -1)
=> 3^(-4-1)
=> 3^-5
=> 1/3^5
=> 1/243 (≠1/27)

Answer is C

Posted from my mobile device

Kinshook · Answer

Asked: If n is a positive integer, then ((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4 =

A (1/3)^(-4n)
B (1/3)^(-4n+1)
C 3^(-4n+ 1)
D 3^(-4n)
E 3^(-4n -1)

((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4 = (-1)^{-4n}(3)^{-4n} + 3^{-4n} + (-1)^{-4n}(3)^{-4n} = 3^{-4n} + 3^{-4n} + 3^{-4n} = 3*3^{-4n} = 3^{1-4n} ; 
Since  (-1)^{-4n} = 1

IMO C

HoneyLemon · Answer

C ,  imo

((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4 = (1/ 3^4n) + (1/ 3^4n) + (1/ 3^4n) = 3 / 3^4n = 3 ^ (1-4n)

Hence c .

coreyander · Answer

Any number raised to a even power will result in a positive value.  
Thus, ignore the negative sign of 3 in the equation. ----(1)

First Part:  ((-3)^{n})^{-4} = (-3)^{-4n} = \frac{1}{(-3)^{4n}} = \frac{1}{3^{4n}}...  (implement (1))

Second Part:  (3^{-n})^{4} = (3)^{-4n} = \frac{1}{3^{4n}}

Third Part:  ((-3)^{-n})^{4} =(-3)^{-4n} = \frac{1}{(-3)^{4n}} = \frac{1}{3^{4n}}...  (implement (1))

Adding all three parts together =  \frac{1}{3^{4n}}+\frac{1}{3^{4n}}+\frac{1}{3^{4n}} 
 \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = \frac{3}{3^{4n}} 
 \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = \frac{1}{3^{4n-1}} 
 \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 3^{-(4n-1)}

\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 3^{-4n+1}

Thus, the answer is (C)

coreyander · Answer

The significance of mentioning   "n is a positive integer"   in the question is:

Any number raised to a even power will result in a positive value.
Thus, we can ignore the negative sign of 3 in the equation

Had that not been mentioned, then n could be 3/4.... n=3/4
and  4n = 4*3/4 = 3

Thus (-3) will have an odd power and you will not be able to neglect the negative sign. 
 
 Forgot to mention this in my previous post.

Babineaux · Answer

IMO ans is C

As all three simplified to  3^(^-^4^n^) ;
Thus  3^(^-^4^n^)  x 3
 3^(^-^4^n^+^1^)

bumpbot · Answer

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.

If n is a positive integer, then ((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If n is a positive integer, then ((-3)^n)^-4 + (3^-n)^4 + ((-3)^-n)^4

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards