For canon, exposure for a 400mm 5.6 on a crop (640mm 5.6) is the SAME exposure as a 400mm 5.6 on a full frame. By using a crop sensor the aperture doesn't magically shrink. Just like taking the center section of a full frame image to give the same view as a crop sensor does not shrink the aperture.
No, the aperture stays the same. Aperture = 400mm/5.6 = 71.43mm. If you're going to call that a 640mm equivalent lens because of the smaller sensor, you have to call it a 640mm/71.43mm = f/9 equivalent f-stop too.