MGMAT - Exponents with negative bases

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

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

put n=0
A -1=1
B 1=1
C 1=1
D 1=1
E 1=-1
So the fight is between A and E.
–2^n = (–2)^-n
for any Positive value of n, LHS is integer and RHS is fraction.
for any negative value of n, LHS is fraction and RHS is integer.
Hence no solution exists.

E
(–2)^-n = –2^-n
Both LHS and RHS will be either fractions or integers.

Hence pick A.

What is OA?

Awesome! OA is indeed A.

I was getting confused between -2^n & (-2)^n -- couldn't understand the difference.

So if I'm getting this right, -x^n will always be - (x^n) i.e. we won't consider the - sign when calculating while (-x)^n will be a figure where the - sign *will* be considered when using the exponent.

Am I right?

Thanks!

jube wrote:Awesome! OA is indeed A.

I was getting confused between -2^n & (-2)^n -- couldn't understand the difference.

So if I'm getting this right, -x^n will always be - (x^n) i.e. we won't consider the - sign when calculating while (-x)^n will be a figure where the - sign *will* be considered when using the exponent.

Am I right?

Thanks!

Yes.. you got it right