Terrorism isn't an ideology. It's a method for waging war.
Being the world's only superpower means that all of our battles will be asymetric. From now on, we can expect each and every one of our enemies to use this method. To take the U.S. on toe to toe is the height of foolishness.
Every one of these "terrorists" probably has friends and family that will respond with anger and violence to our own attacks. Attack, reattack, rinse, lather, repeat.
We have but one solution... genocide. Yeah baby... kill 'em all.