"Authorizing"/"Downloading"/"Waiting for install" for a long time OR "error 40x" can mean your card/other payment type wasn't accepted by Google - please check emails from Google Play with details on the order. Please follow the links in Google Play email sent to your phone google account to resolve card issue.
If you're experiencing problems with the purchase via Google Play store, you can try alternative purchase method (which accepts wider range of cards and other payment methods (Poweramp v3) and doesn't require Google Services on the device) at Poweramp website http://powerampapp.com
