How to calculate attack and damage modifiers for level 1 barbarian with bite attack and great axe?

Question

I'm making a level 1 Half-Orc Unchained Barbarian, with an 18 STR and power attack. I took the tusked racial trait, giving him a 1d4 bite attack to go along with a 1d12 great axe.

How would I calculate the following attack bonuses and modifiers for the following situations? I'm a bit confused on the specifics of the inclusion of bite attacks. I'll include my attempts in figuring them out.

Single great axe attack with power attack
+4 attack (+4 STR, +1 BAB, -1 Power Attack)
1d12+9 damage (+4 STR, +2 2-Hands, +2 Power Attack, +1 2-hand power attack)

Single bite attack with power attack
+4 attack (+4 STR, +1 BAB, -1 Power Attack)
1d4+6 damage (+4 STR, +2 Power Attack)

Full power attack with Great Axe and Bite
+4 axe attack (+4 STR, +1 BAB, -1 Power Attack)
1d12+6 axe damage (+4 STR, +2 Power Attack)
-1 bite attack (+4 STR, +1 BAB, -1 Power Attack, -5 secondary)
1d4+4 bite damage (+2 half STR, +2 Power Attack)

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I'm assuming the Unchained Rage adds +2 attack and +2 damage to all of those calculations?

Answer 1

Full-attack damage

Greataxe

The greataxe is still a two-handed weapon, and

Creatures with natural attacks and attacks made with weapons can use both as part of a full attack action (although often a creature must forgo one natural attack for each weapon clutched in that limb, be it a claw, tentacle, or slam). Such creatures attack with their weapons normally but treat all of their available natural attacks as secondary attacks during that attack, regardless of the attack’s original type.

^{(Natural Attacks, emphasis mine)}

So your greataxe should be dealing the same 1d12+9 damage in the full-attack that it does with the standard-action attack.

This would be different if you were using a claw attack rather than a bite—with a claw, it would use a hand (“often a creature must forgo one natural attack for each weapon clutched in that limb”). Since the greataxe is a two-handed weapon, it can’t be used with one hand, so using a claw would mean not using the greataxe. But since a bite is not on a limb, using it does not interfere with the greataxe attack at all.

Bite

You have bite as a secondary weapon, correctly applying the −5 penalty to attack and halving the Strength bonus to damage. However, you missed or forgot that your damage bonus from Power Attack is halved on a secondary natural weapon, so instead of getting +2 as it does in a standard-action attack, it gets +1, for a total of 1d4+3.

Otherwise, correct

The rest of your calculations are correct, and you are correct about the effect of unchained rage.