This problem has to do with android studio bipmap folder. I read the doccumentation http://developer.android.com/guide/practices/screens_support.html, and I understand that we use the bipmap folder ldpi - xxxhdpi using the following scale 3:4:6:8:12 for the images. I started with a very large picture and scaled it down with Photoshop, creating one image for each of the folder using the scale above, the only thing I'm confused about are the limitations on the pixel per inch (PPI) for each of the corresponding folders. Since lower resolution screens, have less pixels across the whole screen I would imagine/anticipate a required change in PPI, and restrictions on it. I apologize in advance if this question has more to do with photography but I'm using it in my coding program.
This is a question for designers, unlike me, but from my experience you need a vector image. I am working on an app now which I used Adobe Fireworks to complete. All of the shapes in the image are vectors shapes so they scale on their own (sort-of speak). Because they are vectors, they do not require resizing.
If you cant do that then consider having different sizes sizes for the@drawer/ or @mipmap/ folder. As to your DPI question, the resolution should be 72 PPI for all sizes of the image. Then RESIZE the IMAGE in Adobe. This will keep the PPI ratio of the image but change the number of pixels it takes to draw it.
You need to do more research on ICONOGRAPHY and the DESIGN guidelines for Android. I have linked the design guidelines home and the iconography (The iconography link applies to all API Levels and is MIT's cached version of the Google page since Google only talks about new API Levels.) Check them out!