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Which of the following is equal to x^k for all positi

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Which of the following is equal to x^k for all positi [#permalink] New post 27 Aug 2018, 08:57
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Which of the following is equal to \(x^k\) for all positive values of x and k ?

A. \((x^\frac{k}{4})^\frac{3}{4}\)

B. \(\frac{x^k}{x^{2k}}\)

C. \(x^\frac{k}{2} + x^\frac{k}{2}\)

D. \((x^\frac{k}{2})^2\)

E. \((x^k)^k\)
[Reveal] Spoiler: OA

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Re: Which of the following is equal to x^k for all positi [#permalink] New post 12 Apr 2019, 08:23
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Carcass wrote:
Which of the following is equal to \(x^k\) for all positive values of x and k ?

A. \((x^\frac{k}{4})^\frac{3}{4}\)

B. \(\frac{x^k}{x^{2k}}\)

C. \(x^\frac{k}{2} + x^\frac{k}{2}\)

D. \((x^\frac{k}{2})^2\)

E. \((x^k)^k\)



A. \((x^\frac{k}{4})^\frac{3}{4}\)
Apply the Power of a Power law to get: \(x^3k\)
No good

B. \(\frac{x^k}{x^{2k}}\)
Apply the Quotient law to get: \(x^{-k}\)
No good

C. \(x^\frac{k}{2} + x^\frac{k}{2}\)
Doesn't simplify to be \(x^k\)
No good


D. \((x^\frac{k}{2})^2\)
Apply the Power of a Power law to get: \(x^k\)
PERFECT!


E. \((x^k)^k\)
Apply the Power of a Power law to get: \(x^{k^2}\)
No good

Answer: D

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Re: Which of the following is equal to x^k for all positi   [#permalink] 12 Apr 2019, 08:23
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