How did rome win the third punic war?

Rome , through the defeat of Carthage , achieved hegemony throughout the Mediterranean since there was no one else to compete with for power .

149 B.C. - 146 B.C. : Carthage was destroyed by Roman forces under the command of Scipio Aemilianus .

By abandoning the strategy of defending the Italian peninsula and getting their asses kicked by Hannibal and taking to fight to a defenseless Carthage.

There waere three Punic Wars, Rome won all three and after the final one destroyed Carthage and sold its inhabitants into slavery so there would be no fourth war.

By building a navy and establishing superior naval tactics to counter the hitherto dominant Carthaginian fleet.