Can a database created in MS SQL Server Express be exported to MS SQL standard?

Yes. Both products are part of Microsoft's standard SQL platform. Simply backup your database on the SQL Express platform and restore the backup on the SQL Standard platform.

It really is that simple. About the only possible issue I can think of that will make it more than a few mouse-clicks or a couple lines of T-SQL is that you will need to specify new locations for the .mdf and .ldf files during the restore process. And that's not exactly rocket science to figure out.