Roger, when you export your database, you cannot have point-in-time recovery in case of a media failure.
You will lose all changes since your last backup. You cannot re-apply the data in the archived redo logs because with an import, your old rowids will get lost. And Oracle keeps book about changes in the redo logs via the rowids.
Also if you search metalink, you'll find a lot of issues with full database exports. I hope you are doing a schema export?
And last but not least: exp and Intermedia don't play together.
exp should be part of your backup strategy nonetheless, because it provides backups on a logical and consistent level.
Depending on your uptime requirements and how dear your data is to you, you might shutdown your database every night and take a cold backup. Otherwise you must look into taking hot backups.