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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
Posts: 59725

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19 Mar 2019, 02:17
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Difficulty:

45% (medium)

Question Stats:

58% (01:32) correct 42% (01:37) wrong based on 50 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) $$\sqrt[81]{x^{80}}$$

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19 Mar 2019, 04:15
2
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) $$\sqrt[81]{x^{80}}$$

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