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A file with the extension .ape, is an audio file compressed using Monkey's Audio. Monkey's Audio is a lossless compression, which means it does not permanently discard data during compression. It achieves compression rates of around 40%.
Since it is lossless, the quality of the audio after compression will be the exact same. There are several players for Monkey's Audio. One of the best is Foobar 2000.
I you need to burn Monkey's Audio as an Audio CD, you can do so with Nero Burning Rom if you download a plugin here.
Related software tools
Foobar 2000 (Freeware)
Foobar is an advanced audio player for audiophiles
Nero Multimedia Suite (Nero Burning ROM) (Shareware)
Nero is the best and most complete DVDR / CDR / Blu-ray all-in-one software