Can a Compound Bow Kill a Bear

Absolutely. Bow hunters regularly hunt bears. From a tree stand.

Can a compound bow take down a bear?

Just like the arrow section: every bow on earth can do the job if it’s strong enough. Nowadays you would choose a compound or recurve bow. If you like to shoot a long-bow it doesn’t matter either.

How strong should a bow be to kill a bear?

A 50-pound bow is totally adequate but may limit your shot opportunities. More important is your arrow and broadhead selection. You want to maximize your effectiveness by selecting a heavy arrow (ideally more than 600 grains), and a solid, tough, and deep-penetrating broadhead.