On your navigation panel, click on Gallactic Powers. Select each of the powers in turn by clicking on their photos, then click on their expansion tab. There, you'll be able to see what they're doing to expand.
If you want to get merits by killing ships in a strike zone or whatever they call it, even if your power isn't expanding or doesn't have one, you can go and oppose somebody that does have one, which is slightly easier, because you get a chance to sort yourself out in the strike zone before choosing sides. In your own power's one, you're dropped straight into the fight. I've had my shields knocked out in shield-tanking Corvette before I even got my first enemy targeted.