Alrighty, so, how much damage would a Rhinoceros Druid Animal Companion, with the level 7 advancement, do on a Powerful Charge if they have Animal Growth and Strong Jaw on them?
2d6 boosted three sizes becomes 6d6.
What exactly Powerful Charge does, is, annoyingly, never explicitly spelled out anywhere. For most quadrupeds, it's double the dice and Str modifier x2, so the powerful charge should be 12d6+2*Str mod
I was under the impression the Rhinos damage dice just becomes 2d8 during a powerful charge
90% of the creatures in the bestiaries that have powerful charge get the regular damage dice of their regular gore attack doubled, and that's what the race builder rules say as well. The exceptions that exist in the bestiaries are one creature that gets triple dice, two that get quadruple, one where the powerful charge is exactly the same as a normal gore, and one that doesn't normally have a gore attack at all.
The only part of powerful charge that is unclear is if normally gets 1.5x Str mod or 2x Str mod. Most creatures that have it get 2x (And one of the creatures that has it at 2x is a Rhinoceros animal companion). Some only get 1.5x (bipeds and quadrupeds that have antlers instead of horns for their gores as far as I can tell). A few have damage that doesn't appear to correspond directly to 1.5x or 2x. The race builder rules (which is the only place that powerful charge comes anywhere close to actually being explained) says it should be 1.5x.
So ignore the 2d8 then?
Well I'm actually curious where you're getting the idea of 2d8 from in the first place.
7th-Level Advancement
Size Large; AC +3 natural armor; Attack gore (2d6); Ability Scores Str +8, Dex –2, Con +4; Special Qualities powerful charge (gore, 2d8).
What source are you pulling that from? Neither the PRD nor the actual Bestiary has the "(gore, 2d8)" written in.
The d20pfsrd
Well, I have no idea where they got that bit of text from. As far as I can tell, they made it up because even the regular (non companion) rhino's powerful charge is double the dice of its standard gore.
So yes, I'd say you should ignore the 2d8. Because it's wrong.
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We're investigating where the numbers came from. As a note, they've been there since early 2011. I am attempting to determine which editor made that change and why now. It could have been an off-hand board post by a designer, or an errata update (which I can't seem to locate) or possibly a guess. If it was a guess the numbers will be removed.