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# Which of the following is equivalent to

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Math Expert
Joined: 02 Sep 2009
Posts: 45223
Which of the following is equivalent to [#permalink]

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23 Jun 2015, 23:35
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Question Stats:

93% (00:41) correct 7% (00:58) wrong based on 105 sessions

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Which of the following is equivalent to $$(\frac{1}{3})^{-4}*(\frac{1}{9})^{-3}*(\frac{1}{27})^{-2}$$?

A. $$(\frac{1}{3})^{-8}$$

B. $$(\frac{1}{3})^{-9}$$

C. $$(\frac{1}{3})^{-16}$$

D. $$(\frac{1}{3})^{-18}$$

E. $$(\frac{1}{3})^{-144}$$

Kudos for a correct solution.

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Intern
Joined: 28 Jan 2013
Posts: 31
Location: United States
GPA: 3.1
WE: Information Technology (Consulting)
Which of the following is equivalent to [#permalink]

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24 Jun 2015, 02:17
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$$(\frac{1}{3})^{-4}$$∗$$(\frac{1}{9})^{-3}$$∗$$(\frac{1}{27})^{-2}$$

$$(\frac{1}{3})^{-4}$$∗$$(\frac{1}{3})^{-6}$$∗$$(\frac{1}{3})^{-6}$$
$$(\frac{1}{3})^{-4-6-6}$$

$$(\frac{1}{3})^{-16}$$

Ans:C
Manager
Joined: 26 Dec 2012
Posts: 146
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: Which of the following is equivalent to [#permalink]

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24 Jun 2015, 10:15
Arranging equation we can write 1/9 = (1/3)^2; 1/27= (1/3)^3 hence we have
(1/3)^-4 *{(1/3) ^-3*2 } * { (1/3)^-2*3}=
(1/3)^-4 * (1/3)^-6 * (1/3)^-6=
(1/3)^-16
Thanks,
Manager
Joined: 19 Jul 2017
Posts: 85
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Re: Which of the following is equivalent to [#permalink]

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02 Sep 2017, 08:45
Bunuel wrote:
Which of the following is equivalent to $$(\frac{1}{3})^{-4}*(\frac{1}{9})^{-3}*(\frac{1}{27})^{-2}$$?

A. $$(\frac{1}{3})^{-8}$$

B. $$(\frac{1}{3})^{-9}$$

C. $$(\frac{1}{3})^{-16}$$

D. $$(\frac{1}{3})^{-18}$$

E. $$(\frac{1}{3})^{-144}$$

Kudos for a correct solution.

1/a^-m = a^m.
So the equivalent form is 3^4 * 9^3 * 27^2= 3^4 * 3^6* 3^6= 3^16

The equivalent in answer form is D 1/3^-16
Director
Joined: 13 Mar 2017
Posts: 609
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Which of the following is equivalent to [#permalink]

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02 Sep 2017, 10:11
Bunuel wrote:
Which of the following is equivalent to $$(\frac{1}{3})^{-4}*(\frac{1}{9})^{-3}*(\frac{1}{27})^{-2}$$?

A. $$(\frac{1}{3})^{-8}$$

B. $$(\frac{1}{3})^{-9}$$

C. $$(\frac{1}{3})^{-16}$$

D. $$(\frac{1}{3})^{-18}$$

E. $$(\frac{1}{3})^{-144}$$

Kudos for a correct solution.

$$(\frac{1}{3})^{-4}*(\frac{1}{9})^{-3}*(\frac{1}{27})^{-2}$$
$$(\frac{1}{3})^{-4}*(\frac{1}{3})^{-3*2}*(\frac{1}{3})^{-2*3}$$
$$(\frac{1}{3})^{-4}*(\frac{1}{3})^{-6}*(\frac{1}{3})^{-6}$$
$$(\frac{1}{3})^{-4-6-6}$$
$$(\frac{1}{3})^{-16}$$

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Re: Which of the following is equivalent to   [#permalink] 02 Sep 2017, 10:11
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