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

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If 2^m = 5 and 5^n = 3, then 3^(1/n)/2^ [#permalink]

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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

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EDIT: Sorry - wrong forum
[Reveal] Spoiler: OA

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

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

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New post 12 Feb 2017, 08:53
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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^   [#permalink] 12 Feb 2017, 08:53
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