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# If m is an integer and x^m = 1/x^m, what is the value of x?

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If m is an integer and x^m = 1/x^m, what is the value of x? [#permalink]
BrentGMATPrepNow
Bunuel
If m is an integer and $$x^m = \frac{1}{x^m}$$, what is the value of x?

(1) x is an integer.
(2) m in a non-zero integer

II. $$x = 1$$, and $$m =$$ any integer, in which case the given equation of satisfied.
III. $$x = -1$$, and $$m =$$ any even integer, in which case the given equation of satisfied.

Case b: $$x = -1$$ and $$m = 2$$. In this case, the answer to the target question is $$x = -1$$

The coloured portion is not limited to m as even integer.
x as -1 gives yes as an answer for all values of m.

$$x^m = \frac{1}{x^m}$$
$$(-1)^3 = \frac{1}{(-1)^3}…….-1=-1$$ YES
If m is an integer and x^m = 1/x^m, what is the value of x? [#permalink]
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