Why is the prefix "bel" rather than "ber" in this case?
This is one of the exceptions of the "ber-" prefix.
[ber-] + [ajar] = belajar
[ber-] + [kerja] = bekerja
It's actually the 'ber' prefix but the word experience consonant gradation.
In my opinion, "belajar" is a word.
Belajar = study