Exporting iPod Video formats on a Mac Pro

I have multiple programs that allow you to export media to multiple iPod formats (classic, nano, touch, etc). Obviously the main difference is the resolution or picture dimensions. My question is this:

Do I need to export a video for each format? Or can I just export a single Higher resolution video in the hopes that the video will be automatically scaled down to the native resolution of the device by that device? In other words, when a user downloads a video from iTunes, does their iPod work with the video whatever the resolution, or does the user have to download a video with the appropriate resolution for his or her device?


Thank you for you help.

They should all support the same formats on the highest resolution, unless that nano is a older one.