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

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SVP
Joined: 11 Sep 2015
Posts: 2049
If 2^m = 5 and 5^n = 3, then 3^(1/n)/2^ [#permalink]

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12 Feb 2017, 06:47
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74% (01:23) correct 26% (02:17) wrong based on 113 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
[Reveal] Spoiler: OA

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Brent Hanneson – Founder of gmatprepnow.com

Math Expert
Joined: 02 Aug 2009
Posts: 5647
Re: If 2^m = 5 and 5^n = 3, then 3^(1/n)/2^ [#permalink]

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12 Feb 2017, 08:38
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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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Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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SVP
Joined: 11 Sep 2015
Posts: 2049
Re: If 2^m = 5 and 5^n = 3, then 3^(1/n)/2^ [#permalink]

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12 Feb 2017, 08:53
Expert's post
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

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_________________

Brent Hanneson – Founder of gmatprepnow.com

Re: If 2^m = 5 and 5^n = 3, then 3^(1/n)/2^   [#permalink] 12 Feb 2017, 08:53
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