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If k^(xy)=1, where k≠0, which of the following must be tru

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If k^(xy)=1, where k≠0, which of the following must be tru

by AAPL » Mon Nov 27, 2017 7:49 am
$$If\ \ k^{xy}=1,\ where\ k\ne0,$$ which of the following must be true?

$$I.\ \ k=1$$
$$II.\ \ x=0$$
$$III.\ \ y=0$$

A. I only
B. II only
C. III only
D. I and II
E. None

The OA is E.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
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by DavidG@VeritasPrep » Mon Nov 27, 2017 7:56 am
AAPL wrote:$$If\ \ k^{xy}=1,\ where\ k\ne0,$$ which of the following must be true?

$$I.\ \ k=1$$
$$II.\ \ x=0$$
$$III.\ \ y=0$$

A. I only
B. II only
C. III only
D. I and II
E. None

The OA is E.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
Test the statements and see if you can falsify them. The only restriction we have is that 2^(xy) = 1. So long as we meet that condition, we have valid numbers to test.

I. Say k = 2. Well, 2^0 = 1, so clearly, k doesn't have to be 1. I is out.
II Say k = 2, x = 1, and y = 0. We'd have 2^(1*0) = 2^0 = 1. Clearly x doesn't have to be 0. II is out.
III Say k =2, x = 0, and y = 1. Now we'd have 2^*(0*1) = 2^0 = 1. Clearly y doesn't have to be 0. III is out.

The answer is E
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