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

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Senior Manager
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Joined: 25 Dec 2018
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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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New post 10 Apr 2019, 12:01
00:00
A
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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
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Re: If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =  [#permalink]

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New post 10 Apr 2019, 15:14
Solution attached.
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If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =  [#permalink]

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New post 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.
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Re: If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =  [#permalink]

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New post 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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Re: If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =   [#permalink] 11 Apr 2019, 06:31
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If (1/27)^9∗(1/2)^a=1/(9∗12^25) , then a =

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