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Simplify (x*(x*(x*x^(1/2)))^(1/3))^(1/3))^(1/3)

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Joined: 02 Sep 2009
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Simplify (x*(x*(x*x^(1/2)))^(1/3))^(1/3))^(1/3)  [#permalink]

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New post 19 Mar 2019, 02:17
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

52% (01:26) correct 48% (01:40) wrong based on 23 sessions

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Re: Simplify (x*(x*(x*x^(1/2)))^(1/3))^(1/3))^(1/3)  [#permalink]

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New post 19 Mar 2019, 04:15
1
Bunuel wrote:
Simplify \(\sqrt[3]{x*\sqrt[3]{x*\sqrt[3]{x*\sqrt{x}}}}\)


(A) \(\sqrt{x}\)

(B) \(\sqrt[3]{x^2}\)

(C) \(\sqrt[27]{x^2}\)

(D) \(\sqrt[54]{x}\)

(E) \(\sqrt[81]{x^{80}}\)


The video solution to the question is explained step-by-step here

Answer: Option A


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Re: Simplify (x*(x*(x*x^(1/2)))^(1/3))^(1/3))^(1/3)  [#permalink]

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New post 19 Mar 2019, 10:41
Let's start from the inside of the given expression.
\(x^\frac{1}{2}* x = x^\frac{3}{2}\)
\(x^\frac{3*1}{2*3} = x^\frac{1}{2}\)


\(x^\frac{1}{2}* x = x^\frac{3}{2}\)
\(x^\frac{3*1}{2*3} = x^\frac{1}{2}\)

\(x^\frac{1}{2}* x = x^\frac{3}{2}\)
\(x^\frac{3*1}{2*3} = x^\frac{1}{2}\)

Hence, choose A.
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Re: Simplify (x*(x*(x*x^(1/2)))^(1/3))^(1/3))^(1/3)   [#permalink] 19 Mar 2019, 10:41
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