As the above posters have said, aminoglycoside + beta lactam synergy is a relatively 'high yield' topic. Perhaps beta lactams increase the penetration of AGs into bacterial cells, but it's not proven/I couldn't find any solid evidence in literature. (and I think some combinations are actually quite ineffective, e.g. piperacillin-gentamicin, where the former causes inactivation of the latter in the kidneys, reducing the half life 3x in-vivo)
I think I also read somewhere (probably in Kaplan) that beta lactams and tetracyclines are antagonistic, although they are combined in certain situations. Gotta love exceptions in medicine eh. First they make rules and then you realise the rules apply only in half the cases.