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If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =

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Senior Manager
Joined: 25 Dec 2018
Posts: 307
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =  [#permalink]

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10 Apr 2019, 12:01
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:45) correct 31% (02:46) wrong based on 26 sessions

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If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =

A. 25
B. 26
C. 37
D. 50
E. 51
Manager
Joined: 21 Feb 2019
Posts: 118
Location: Italy
Re: If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =  [#permalink]

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10 Apr 2019, 15:14
Solution attached.
Attachments

Scan.pdf [275.99 KiB]

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MEMENTO AUDERE SEMPER
Intern
Joined: 05 Apr 2019
Posts: 7
If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =  [#permalink]

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10 Apr 2019, 18:12
lucajava wrote:
Solution attached.

how does 2^2 (3) = (1/3)^25 and (1/2)^50 ? I guess you're multiplying 25 X 2= 50 but whats the rule I should follow so I know I have to do this next time.
Thank you.
Manager
Joined: 21 Feb 2019
Posts: 118
Location: Italy
Re: If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =  [#permalink]

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11 Apr 2019, 06:31
1
So, $$12 = 2^2 * 3$$;

$$12^{-1} = \frac{1}{12}$$;

$$12^{-1} = 2^{-2} * 3^{-1}$$

$$12^{-25} = 2^{-2*25} * 3^{-1*25}$$

$$(\frac{1}{12})^{25} = (\frac{1}{3})^{25} * (\frac{1}{2})^{50}$$

thealpine Hope it's clear now.
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MEMENTO AUDERE SEMPER
Re: If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =   [#permalink] 11 Apr 2019, 06:31
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