how do I back up my exchange emails on the icloud

You can't select to simply back up Exchange emails to iCloud. You can run a full backup of your iPhone to iCloud. That way if you need to restore your phone then all of your settings would be restored and you don't need to re-setup your email settings.

Your subject line asked how you back up Exchange to iCloud and then you asked about syncing Exchange and Google. If you are wanting to sync between Exchange and Google I would check out some Google discussion boards.