Canon SX50 HS and Canon SX40 HS cameras use NB-10L lithium rechargeable battery. This is another great change from old Canon SX super-zoom cameras like SX10 and SX20. These NB-10L lithium rechargeable batteries are not expensive unless you need Original Canon NB-10L lithium rechargeable battery which cost you around 40$. But you there are other brands which sell same battery for less than 15$. So no point of buying these batteries from Canon but you can find cheaper options at Amazon. Like one I have displaying on left side. That it kit is only 17 USD and it has 2 NB-10L lithium rechargeable batteries and Car charger which can be very very handy in outdoors.
Main reason Why these NB-10L lithium rechargeable battery is better, because lithium rechargeable batteries had low self discharge rate. Which means battery will stay alive for long time than rechargeable AA batteries. Also you can take lot more photos with these lithium rechargeable batteries than with AA batteries. These days one of these battery cost you less than 10 USD so these are not expensive either. It's a common myth that lithium rechargeable batteries are more expensive. Maybe years before but not anymore.
You can take around at least 400-600 photos spending on charge. Having three of these batteries will enough for even week long vacation or trip. I don't think most of time time you will even get chance to take over 500 photos unless you are a professional photographer. I check around and it seems these Photive NB-10L Battery are pretty good. You can buy separate battery for 10$ but for 17$ you can get 2 batteries plus charger. If you are an Owner of Canon SX40 or Canon SX50 camera then these are the best replacement batteries for you.