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If 2^m = 5 and 5^n = 3, then 3^(1/n)/2^

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Joined: 12 Sep 2015
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If 2^m = 5 and 5^n = 3, then 3^(1/n)/2^  [#permalink]

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New post 12 Feb 2017, 07:47
1
Top Contributor
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A
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E

Difficulty:

  35% (medium)

Question Stats:

71% (01:27) correct 29% (02:21) wrong based on 139 sessions

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If \(2^m= 5\) and \(5^{1/n} = 3\), then \(\frac{3^n}{2^{-2m}}\) =

A) 1/25
B) 1/5
C) 5
D) 25
E) 125

* kudos for all correct solutions

EDIT: Sorry - wrong forum

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Brent Hanneson – GMATPrepNow.com
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Re: If 2^m = 5 and 5^n = 3, then 3^(1/n)/2^  [#permalink]

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New post 12 Feb 2017, 09:38
1
GMATPrepNow wrote:
If \(2^m= 5\) and \(5^{1/n} = 3\), then \(\frac{3^n}{2^{-2m}}\) =

A) 1/25
B) 1/5
C) 5
D) 25
E) 125

* kudos for all correct solutions

EDIT: Sorry - wrong forum


Hi,
Let's convert the equations given to fit into \(\frac{3^n}{2^{-2m}}\) ..

\(2^m= 5, ..... 2^{2m}=5^2=25\) and \(5^{1/n} = 3......(5^{1/n})^n=3^n.....3^n=5\)...

\(\frac{3^n}{2^{-2m}}=3^n*2^{2m}\) ..
Substitute the values in \(3^n*2^{2m}=5*25=125\)

E
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Joined: 12 Sep 2015
Posts: 2889
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Re: If 2^m = 5 and 5^n = 3, then 3^(1/n)/2^  [#permalink]

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New post 12 Feb 2017, 09:53
Top Contributor
GMATPrepNow wrote:
If \(2^m= 5\) and \(5^{1/n} = 3\), then \(\frac{3^n}{2^{-2m}}\) =

A) 1/25
B) 1/5
C) 5
D) 25
E) 125


Given: \(2^m= 5\)
We need to determine the value of \(2^{-2m}\)
So, take \(2^m= 5\) and raise both sides to the power of -2
We get: (2^m)^(-2) = 5^(-2)
Apply Power of a Power rule to get: 2^(-2m) = 5^(-2)

Given: \(5^{1/n} = 3\)
We need to determine the value of 3^n
So, take \(5^{1/n} = 3\) and raise both sides to the power of n
We get: [5^(1/n)]^n = 3^n
Apply Power of a Power rule to get: 5^1 = 3^n

So, (3^n)/2^(-2m) = (5^1)/[(5^(-2)]
= 5^3
= 125

Answer: E

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Re: If 2^m = 5 and 5^n = 3, then 3^(1/n)/2^ &nbs [#permalink] 12 Feb 2017, 09:53
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