Simplify (x*(x*(x*x^(1/2)))^(1/3))^(1/3))^(1/3) : Problem Solving (PS)

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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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19 Mar 2019, 02:17

00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:26) correct

48% (01:40) wrong

based on 23 sessions

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

Spoiler: OA

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

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19 Mar 2019, 04:15

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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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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