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

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Founder
Joined: 18 Apr 2015
Posts: 6200
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Kudos [?]: 1199 [0], given: 5712

Which of the following is equal to x^k for all positi [#permalink]  27 Aug 2018, 08:57
Expert's post
00:00

Question Stats:

76% (00:36) correct 23% (00:47) wrong based on 21 sessions
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

_________________
GRE Instructor
Joined: 10 Apr 2015
Posts: 1652
Followers: 57

Kudos [?]: 1575 [1] , given: 8

Re: Which of the following is equal to x^k for all positi [#permalink]  12 Apr 2019, 08:23
1
KUDOS
Expert's post
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

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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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