Hi, In the current app, you will have to export via email using the envelope icon in the lower left of the window and then move the file to Google drive.
We are currently in the process of designing an all-new Audio Exam app. Our priorities are adding Android, computer, Chromebook versions, and many new features. The new features we are working on include a file management system that you will probably be delighted with. We're working hard, but I can't tell you when we will have it finished. Stay tuned.