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If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =

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Joined: 18 Feb 2019
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Location: India
GMAT 1: 490 Q47 V13
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If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =  [#permalink]

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New post 29 Mar 2019, 00:23
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Difficulty:

  55% (hard)

Question Stats:

59% (02:18) correct 41% (02:10) wrong based on 17 sessions

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If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =

A. 1
B. 2
C. 3
D. 4
E. 5
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Joined: 02 Aug 2009
Posts: 7575
Re: If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =  [#permalink]

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New post 29 Mar 2019, 00:46
kiran120680 wrote:
If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =

A. 1
B. 2
C. 3
D. 4
E. 5



Let us take each separately ..
(I) \((\frac{1}{2})^a∗(\frac{1}{2})^b=(4)^−2=(\frac{1}{4})^2\)..
\((\frac{1}{2})^{a+b}=(\frac{1}{4})^2=(\frac{1}{2})^4\)
By equating the power of (1/2) on both sides, we get a+b=4.
(II) \((\frac{1}{5})^a∗(\frac{1}{125})^b=(5)^−6=(\frac{1}{5})^6\)..
\((\frac{1}{5})^{a+3b}=(\frac{1}{5})^6\)
By equating the power of (1/5) on both sides, we get a+3b=6

Thus, we have two equations..
a+b=4 and a+3b=6
Subtracting 1 from 2 .. a+3b-(a+b)=6-4=2......2b=2 or b=1
So, a+1=4 or a=3.

Therefore, \(\frac{a}{b}=\frac{3}{1}=3\)

C
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Re: If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =   [#permalink] 29 Mar 2019, 00:46
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If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =

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