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If x is not = to 0, what is the value of (x^m/x^n)^5?

\((\frac{x^m}{x^n})^5=(x^{m-n})^5=?\)

(1) n - m = 2 --> m - n = -2 --> \((x^{m-n})^5=(x^{-2})^5\). Not sufficient.

(2) x^2 = 1/4. Not sufficient.

(1)+(2) From (2) we have that \(x^{-2}=4\), thus from (1) \((x^{-2})^5=4^5\). Sufficient.

Answer: C.


Sorry Bunuel I understand all the situation but in stat 2) we have x = + - 1/2 ???? or in this case we take the value as such ?? x^2=1/4 and why in the latter case ??

Yes, from (2) we have that x=1/2 or x=-1/2. But to find the value of \((x^{-2})^5\) it's sufficient to know the value of \(x^{-2}\), which is 4.

Hope it's clear.
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ohhh yup

\(x^2=1/4\) OR \(1/x^2=4\) OR \(x^-2=4\) (the same thing). Right. true

Thanks :)
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