First off, tell them about it on your app. Then do what you can to get it removed. The FBI database will still show you were charged, but at least you should be able to show that it was dismissed or expunged if you do your homework. Every state is different, check the local court website. I have not heard how to get things off of the FBI database, so focus on the local stuff first.
If you do the paperwork to get it sealed/dismissed/expunged and then wait to for the local court to approve your petition, and then submit your app, it may be easier with AE. You'll be able to say that it was dismissed/expunged up front on the app.