This is a big deal. So pay attention. You may have never run your battery dry shooting pictures at home. But you may very well in Africa. Around every corner is something new and trust me you will be sick to your stomach if you encounter something you can not take a picture of. Autofocus, long lenses, stabilization and video all munch on power. So make sure you have enough with you because there is no place to buy batteries once you get going.
I shoot Canon and Sony but let's use my canon as an example. I usually take 4-5 batteries with me. They're small and rechargeable. I carry them in my overhead bag since lithium batteries are illegal (and dangerous) to store in your luggage during a flight. I charge them all before I leave. I take TWO chargers with me. One that plugs into the wall, and one that plugs into a cigarette lighter outlet. You can find these on amazon for your specific camera model. Why? Redundancy. If one fails, I'm not screwed. And then, most cameras allow you to charge their batteries right through the camera. I don't do this but you may consider it as your "backup".
Also, depending on where you stay will determine how you charge your batteries. If you are in a big lodge or one of the fancy hotels, they have power all the time so no problem. But even so, it takes about 2 hours to charge a battery so you may not be able to refresh everything overnight unless you like getting up every two hours and changing batteries.
If you have chosen one of the more organic tented lodging options (they're great, check them out!) you may not have 24 hour power. These camps often only run their generators for 12 hours or so a day and shut down after about 10pm. That limits your charging time. So inquire. In either case you will need a plug adapter to change over your USA plug to the one that works in Tanzania. Take two, they're small. Again... Amazon.
Take a small American extension cord with you. Yes, you'll have power... but NOT multiple outlets. You're going to want to charge several things at a time. Get an extension cord that has several outlets on one end. You'll thank me.
I come prepared to charge batteries at night. But I also take a cigarette outlet charger as well. Your safari vehicle runs off a normal 12 volt battery and it will have an cigarette outlet. You can charge a battery (or two if you buy a splitter) as you drive around the Serengeti.
On rare occasions, the cigarette lighter outlet in your vehicle may not work. Want to be super anal and prepared? Buy a small pair of alligator clips, a cigarette outlet and about 10 feet of lamp cord and make a cable that you can hook directly to the vehicle's battery and run back inside the vehicle. This is a little overkill... but we do it anyway. So far, we've only used it once. But we DID have to use it once. And remember... don't forget to charge your batteries every night if you can.