It uses a pack of rechargable AAs, I have an HP-45 (the immediate successor, with the same battery pack) and replaced the original NiCD cells with NiMH. When I got it the batteries were clearly already a few decades old. AAs NiCDs were pretty common back then, I have an old TI and Soviet-made Electronika calculator that also use them.
Right. It mostly wasn't a problem so long as you remembered to charge them before exams, etc. In college, I'd still bring a slide rule to final exams as backup just in case something happened although I never had a problem.
I started college just as scientific calculators were appearing on the scene. I had a TO for a couple of years because the HPs were still so expensive but I was able to pickup an HP-55 after a bit for a relatively affordable price (still probably talking about high 3 digits in today's dollars). That's what I used until I bought an HP-41CV when I went back to school and needed a more programmable calculator.
To add some context: essentially all scientific calculators with LED or VFD displays had rechargable NiCd batteries and plug packs. Typical engineer mostly used them plugged into wall. (And then there was my dad who used his IIRC Sharp VFD scientific calculator as charger for AA NiCd cells well into late 90's)