This is no different than previous versions of Windows, and has nothing to do with UAC.
That external drive's file system was created by an OS other than your Windows install, so you don't have permissions to get at it.
So you don't want to "get rid of administrator permissions" but instead give your user permission to access those files/folders.
You have to take ownership and/or give yourself permissions to the folder/files on that drive., and form there you'll be able to use them without these pop-ups.
See this existing SU question, and it's answers, to figure out how to grant yourself permission:
How do I get permissions to delete files on Windows 7?