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# GMATprep question

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Intern
Joined: 17 Mar 2008
Posts: 12

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01 Jun 2009, 08:42
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If $$(\frac{1}{5})^m*(\frac{1}{4})^{18}= \frac{1}{2*10^{35}}$$, what is m equal to?

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Manager
Joined: 14 May 2009
Posts: 187

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01 Jun 2009, 14:37
1
dakhan wrote:
If $$(\frac{1}{5})^m*(\frac{1}{4})^{18}= \frac{1}{2*10^{35}}$$, what is m equal to?

$$(\frac{1}{5})^m*(\frac{1}{4})^{18}= \frac{1}{2*10^{35}}$$
$$5^{-m}*(4)^{-18}= 2^{-1}*10^{-35}$$
$$5^{-m}*(2*2)^{-18}= 2^{-1}*(2*5)^{-35}$$
$$5^{-m}*(2^2)^{-18}= 2^{-1}*2^{-35}*5^{-35}$$
$$5^{-m}*(2)^{-36}= 2^{-1}*2^{-35}*5^{-35}$$
$$5^{-m}*(2)^{-36}= 2^{-36}*5^{-35}$$
$$5^{-m}*(2)^{-36}= 5^{-35}*2^{-36}$$
$$==> m=35$$
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Intern
Joined: 17 Mar 2008
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01 Jun 2009, 18:38
awesome....seems like a complicated problem from its solution but quite easy once you actually work it out. thanks.

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Re: GMATprep question &nbs [#permalink] 01 Jun 2009, 18:38
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