Dropbox for Android app has been updated to version 188.8.131.52. Included the ability to export files to SD card, improved support for Android L and faster search performance.
It takes just a few steps: start by tapping the “Quick Action” button to the right of the file you want to export, select “More”, then “Export”, and tap “Save to Device” to pick your external SD card. (If you don’t see your external SD card listed there, choose the menu within the “Save to” screen, followed by “Settings” and then “Display advanced devices”.)
The update will be live in the Play Store soon, but participants in the early update program are getting the new version right now.
Source from The Dropbox Blog [A new Dropbox for Android: export files to your SD card]