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# If a >= 0, then ((a^(1/2))^(1/3))^(1/4))^18 =

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Math Expert
Joined: 02 Sep 2009
Posts: 52390
If a >= 0, then ((a^(1/2))^(1/3))^(1/4))^18 =  [#permalink]

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30 Apr 2018, 08:04
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:02) correct 19% (01:06) wrong based on 42 sessions

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If $$a \geq 0$$, then $$(\sqrt[4]{\sqrt[3]{\sqrt{a}}})^{18}=$$

A. $$a^{\frac{39}{2}}$$

B. $$a^{\frac{9}{4}}$$

C. $$a^{\frac{4}{3}}$$

D. $$a^{\frac{3}{4}}$$

E. $$a^{\frac{2}{3}}$$

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Joined: 04 Jan 2015
Posts: 2457
Re: If a >= 0, then ((a^(1/2))^(1/3))^(1/4))^18 =  [#permalink]

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30 Apr 2018, 21:15

Solution

Given:
• a≥0

To find:
• The value of $$(^4√^3√√a)^{18}$$

Approach and Working:
• The given expression can be simplified as follows:
o $$(^4√^3√√a)^{18}$$
= $$(((a)^\frac{1}{2})^\frac{1}{3})^\frac{1}{4})^{18}$$
=$$(((a)^\frac{1}{6})^\frac{1}{4})^{18}$$
=$$((a)^\frac{1}{24})^{18}$$
=$$(a)^\frac{18}{24}$$
= $$a^\frac{3}{4}$$

Hence, the correct answer is option D.

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Re: If a >= 0, then ((a^(1/2))^(1/3))^(1/4))^18 = &nbs [#permalink] 30 Apr 2018, 21:15
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