The power output is directly proportional to either the volume, mass, or the surface area of the neutronium core. That means it's either an X² or X³ function, which makes it an exponential function. I believe it's a cubic function myself. If so, the fact that it's a thousand times as big as anything the UNS can safely build means it's 1,000,000,000 times as powerful as anything they can build. Presumably, the biggest and most powerful (and, according to Howard), the most finely controlled annie plants are on battleplates, Oisri is far more powerful than 1,000,000,000 battleplates. That's because Howard has stated that A bunch of annie plants don't add up to the same as one big annie plant of the same power. This makes sense, since the light-speed delays would tend to cause the various gravity fields to interfere destructively. Hypernet nodes wouldn't help, because they are subject to interference from gravitic fields.
Howard, could you please ask a Kevyn or a Gav? I'm sure one of them can spare the God of the Schlockiverse some time.
In my hard mathematics classes, I learned that functions of the form:
y = kx^n and y = e^nx are both
Technically, we don't actually know that power is directly proportional to any of those. We just know an exponential curve is involved.
My point was, Captain Gasca might have meant that there is a 'normal' exponential relationship for power, like radius squared or radius cubed, correlating to surface area or volume
Or, there might be additional factors we don't know about, and the exponential relationship might be even better: what if it's actually r^4 or even r^6?
If the power relationship were higher than r^3, large power plants would be INCREDIBLY impressive, because their power could not be matched by multiple alternate plants of a total equal volume.
Sorry, but in comp sci I was taught that an exponential function is (N ^ x).