couldn't figure this...

[Night reader]

Each of the following equations has at least one solution EXCEPT:

A. -2^n = (-2)^-n
B. 2^-n = (-2)^n
C. 2^n = (-2)^-n
D. (-2)^n = -2^n
E. (-2)^-n = -2^-n

[GMATGuruNY]

Each of the following equations has at least one solution EXCEPT:

A. -2^n = (-2)^-n
B. 2^-n = (-2)^n
C. 2^n = (-2)^-n
D. (-2)^n = -2^n
E. (-2)^-n = -2^-n

Plug n=0 and n=1 into all the answer choices:

A. -2^n = (-2)^-n
n=0:
-(2^0) = (-2)^-0
-1 = 1. Doesn't work.

n=1:
-(2^1) = (-2)^-1
-2 = -1/2. Doesn't work.
Hold onto A.

B. 2^-n = (-2)^n
n=0:
2^-0 = (-2)^0
1=1.
n=0 is a solution. Eliminate B.

C. 2^n = (-2)^-n
n=0:
2^0 = (-2)^-0
1=1.
n=0 is a solution. Eliminate C.

D. (-2)^n = -2^n
n=1:
(-2)^1 = -(2^1)
-2 = -2.
n=1 is a solution. Eliminate D.

E. (-2)^-n = -2^-n
n=1:
(-2)^(-1) = -(2^-1)
-1/2 = - 1/2
n=1 is a solution. Eliminate E.

The correct answer is A.

[gmatmachoman]

@Mitch,

Y should i use n =1, can't i deduce it with n= 0 for A itself??

[GMATGuruNY]

@Mitch,

Y should i use n =1, can't i deduce it with n= 0 for A itself??

The safest strategy is to eliminate the four answer choices for which there is a solution; the correct answer will be the remaining answer choice. I suggested plugging in n=1 and n=0 because these values seemed likely to work in some of the answer choices. Since n=0 works in B and C, and n=1 works in D and E, the correct answer must be A.

[Night reader]

Almost intuitively I started with plugging 0 at the first sight on this problem in exam (CAT). But I couldn't get it, as 0 is non -ve nor +ve, so got stuck with the sign differentiation All choices seemed working for me

just found useful link https://www.tutorvista.com/math/negative ... zero-power