Problem Solving

akshatgupta87 wrote:Someone explain...

Picking number approach can be used here. Put simple values like n = 0, n = 1 in each of the given answer choices.
(A) n = 0: -2^0 = (-2)^(-0) implies -1 = 1
n = 1: -2^1 = (-2)^(-1) implies -2 = -0.5
It can be seen that the given equation does not have a solution. So, this should be the correct answer. You can check for other choices for clarification.

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

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

(D) n = 0: (-2)^(0) = -2^(0) implies 1 = -1
n = 1: (-2)^1 = -2^(-1) implies -2 = -2. So, n = 1 is a solution.

(E) n = 0: (-2)^(-0) = -2^(-0) implies 1 = -1
n = 1: (-2)^(-1) = -2^(-1) implies -0.5 = -0.5. So, n = 1 is a solution.

Hence, it can be seen that only answer choice A does not have a solution.

The correct answer is A.