That lapotp has a maximum of 2gig of RAM you can use, so there is no point installing a 64bit operating system on it. But it should run. The other issue is that there are no 64bit drivers for it from ASUS so even if it installs, the hardware will probably have issues.
 

Asus_USA

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May 1, 2013
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I would not recommend this as we do not have any Windows 7 64-bit drivers for this specific model. You might run into some issues getting everything to work properly.