How was Rome finally able to defeat Carthage and what did they do to the city?

After the disaster at Cannae, the Romans avoided battle in Italy and frustrated Hannibal. At the same time, the Romans raised an army and attacked the Carthaginians closer to home and their main spheres of influence, thus drawing off Hannibal and his forces. The final battle at Zama saw a well provisioned and led Roman army defeat a bedraggled Carthaginian force that had been rapidly transported and composed before the battle.