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# ((a^2)^6)^(1/3) = ?

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Math Expert
Joined: 02 Sep 2009
Posts: 65808

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02 Jul 2020, 01:44
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Difficulty:

5% (low)

Question Stats:

94% (00:25) correct 6% (00:33) wrong based on 36 sessions

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$$\sqrt [3] { (a^2)^6}=?$$

(A) $$a^2$$

(B) $$a^4$$

(C) $$a^5$$

(D) $$a^9$$

(E) $$a^{11}$$

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Manager
Joined: 05 Oct 2014
Posts: 54
Concentration: Technology, Entrepreneurship

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02 Jul 2020, 01:47
(a^2)^(6/3)

(a^2)^2
a^4

Option : B

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Manager
Joined: 12 Oct 2019
Posts: 55

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02 Jul 2020, 01:54
2
$$\sqrt [3] { (a^2)^6}= \sqrt [3] { a^{2 \times 6}} = \sqrt [3] { a^{12}} = a^{(12/3)} = a^4$$

OA, B

Bunuel wrote:
$$\sqrt [3] { (a^2)^6}=?$$

(A) $$a^2$$

(B) $$a^4$$

(C) $$a^5$$

(D) $$a^9$$

(E) $$a^{11}$$
Director
Joined: 16 Feb 2015
Posts: 657
Location: United States

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02 Jul 2020, 01:57
Explanation:
= (a^2)^6/3
= (a^2)^2
= a^4

IMO-B
GMATWhiz Representative
Joined: 07 May 2019
Posts: 984
Location: India

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02 Jul 2020, 02:07
Bunuel wrote:
$$\sqrt [3] { (a^2)^6}=?$$

(A) $$a^2$$

(B) $$a^4$$

(C) $$a^5$$

(D) $$a^9$$

(E) $$a^{11}$$

Solution

• $$(a^2)^6 = a^{2*6} = a^{12}$$

• Therefore, $$\sqrt[3]{(a^2)^6} = \sqrt[3]{a^{12}} = (a^{12})^{\frac{1}{3}} = a^{12* \frac{1}{3}} = a^4$$

Thus, the correct answer is Option B.
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Joined: 03 Jun 2019
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02 Jul 2020, 03:00
Bunuel wrote:
$$\sqrt [3] { (a^2)^6}=?$$

(A) $$a^2$$

(B) $$a^4$$

(C) $$a^5$$

(D) $$a^9$$

(E) $$a^{11}$$

$$\sqrt [3] { (a^2)^6}= a^{\frac{2*6}{3}} = a^4$$

IMO B
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Re: ((a^2)^6)^(1/3) = ?   [#permalink] 02 Jul 2020, 03:00