i think the major part is military ships as well as military techs  (social buildings and population i think play a low role for score) the ai tends to put a lot of weight towards military atm verses a human player who will probobly  go more for social construction.

on top of that higher levels of ai start with more techs and bonus's to resources so they can build stronger, faster, units more often however it should be easy to outpace them once you get your stride going

Now I'm at 7k and the Iridium are at 36k?  This seems strange, I've been building a ton of military ships and the economy-focused race is 7 times my power.  Somethings weird with these numbers.

,  I notice that my power number was dropping relative to the AI in a situation in which I knew by checking that I was outproducing them.   Very mysterious.   

It took a bit but I realized to my horror that I had been using my template to build ships instead of the ship design.   So I had built a bunch of empty ships.   I don't know how I did this...probably a naming screw up.   Our minister of production was sacked, clearly the whole thing was a military-industrial money grab scam on the government.

After fixing this I rapidly overtook the other empires in power, as my production level was very high.   I also upgraded a lot of the empty shells and decommissioned a bunch of others.

Embarrassing.   But it does again to me indicate that the power number is mostly military attack/defense.