Each of the following equations has at least...

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

$$A.\ -2^n=-2^{-n}$$
$$B.\ 2^{-n}=-2^n$$
$$C.\ 2^n=-2^{-n}$$
$$D.\ -2^n=-2^n$$
$$E.\ -2^{-n}=-2^{-n}$$

The OA is A.

I'm confused with this PS question. Experts, any suggestion, please? How can I determine the solution of this question? Thanks in advance.
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by ErikaPrepScholar » Fri Feb 02, 2018 7:28 am
I don't think this problem is written correctly. As it is currently written, if n=0 for A:
$$-2^n=-2^{-n}$$
$$-2^0=-2^{-0}$$
$$-2^0=-2^0$$
$$-1=-1$$
So there is a solution for A, which means it can't be the correct answer.

Similarly, D and E are pretty obvious wrong answers since both sides of the equation are identical - this means that any number will work for n.

I believe the answer choices are meant to be written as:

$$A.\ -2^n=(-2)^{-n}$$
$$B.\ 2^{-n}=(-2)^n$$
$$C.\ 2^n=(-2)^{-n}$$
$$D.\( -2)^n=-2^n$$
$$E.\ (-2)^{-n}=-2^{-n}$$

If this is the case, we can solve D and E with n=1 and B and C with n=0, while A cannot be solved, making it the correct answer.
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