If you're wondering why everyone is downvoting this post, this is a good place to start. While there are some existential threats that humanity could fight against after they're out of the bag (plagues, for instance), post-intelligence-explosion AI is very probably not one of them.

(Of course, an AI might be able to pose a threat even without being capable of recursive self-improvement, and in that case the threat might conceivably be significant but not beyond human capacities. But your particular scenario is more a cheesy sci-fi pitch than a realistic hypothetical.)