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I'm not sure what you're asking. If the natural attack says to use 1½ times your Strength bonus on damage, you gain and extra 50% damage from Power Attack. If the natural attack says to use ½ your Strength bonus on damage, you only gain half the damage bonus from Power Attack.
If the bite attack is primary, it doesn't get an extra bonus from Power Attack. If it is secondary, it only gets half the bonus damage from Power Attack.
Natural attacks and natural weapons are essentially the same thing; the two terms are often used in the same way that an "attack with a sword" and "a sword" typically mean the same thing when you're talking about bonuses to damage or what have you. A bite is a natural weapon. Biting someone is a natural attack. (I have said the word "natural" in my head so many times now that it sounds funny. Natural. Hee hee.)
When you power attack, all your attacks suffer the penalty to hit, and gain a bonus to damage. If you attack with a sword and bite, the bite becomes a secondary attack; it's made at a -5 to hit, with an additional -1 for power attack. As a secondary attack it also deals 1/2 your strength bonus, and 1/2 the power attack bonus (in this case, 1 point of damage from power attack).
Ok, the Combat section of the PRD says:
"Natural Attacks: Attacks made with natural weapons, such as claws and bites, are melee attacks that can be made against any creature within your reach (usually 5 feet). These attacks are made using your full attack bonus and deal an amount of damage that depends on their type (plus your Strength modifier, as normal). You do not receive additional natural attacks for a high base attack bonus. Instead, you receive additional attack rolls for multiple limb and body parts capable of making the attack (as noted by the race or ability that grants the attacks). If you possess only one natural attack (such as a bite—two claw attacks do not qualify), you add 1–1/2 times your Strength bonus on damage rolls made with that attack."
That's on page 182 of the Core Rulebook. If you go to the Combat section of the PRD:
http://paizo.com/pathfinderRPG/prd/combat.html
and do a search on that page for "natural weapon" the very first instance of that text is the paragraph I quoted above. Also, if you look up "natural attacks" in the Core Rulebook's index, it'll point you at page 182 (quoted above).
Assume an Animal Companion with Claw/Claw/Bite and Power attack with <+4 BAB:
On a full attack, the Power Attack will reduce the chance to hit on all 3 attacks by 1 and increase each attack's damage by 2 (-1/+2) as, in this case, they are all Primary Natural attacks.
If the same animal somehow gained a Hoof attack, which is typically a Secondary Natural Weapon, the Hoof would be at -1/+1, as it is treated similarly to an off-hand attack from a 2 weapon attack.
A bite, however, normally gets x1.5 Str to damage, so it would get +3 damage instead of +2 damage from the Power Attack.
If a critter has more than one natural attack or attack forms, sometimes one attack or form of attack is 'Primary' while the others are 'Secondary'. Some critters have more than one attack form that are treated as primary. You'll have to check the particular bestiary entry.
If a critter is capable of wielding a manufactured weapon and chooses to do so, this causes his other natural attacks to be treated as 'Secondary'.
The bonus power attack gives depends in part on the natural attack being primary or secondary. However, once power attack is declared, its effects apply to ALL attacks made until the start of the critter's next turn when it gets to again declare if power attack is being used.
A bite, however, normally gets x1.5 Str to damage, so it would get +3 damage instead of +2 damage from the Power Attack.
Bite attacks on Dragons gain 1 1/2 xSTR, but not for most creatures.
Thanks for the replies.
Don't bite attacks only do 1.5 x DMG if they are the only attack the creature performs that turn?
Natural attacks do 1.5 STR damage if it's the only attack option the critter has, such as a bite. However, if the critter has a bite and 2 claw attacks listed, even if they can only take a single attack they only get the regular STR damage.
Thanks for the replies.
Don't bite attacks only do 1.5 x DMG if they are the only attack the creature performs that turn?
Most of the time a creature with only one primary attack does 1.5 str damage to make up for the lack of multiple attacks, but the power attack feat never says if you have more than one attack that the 1.5 strength rule does not apply.
You can choose to take a –1 penalty on all melee attack rolls and combat maneuver checks to gain a +2 bonus on all melee damage rolls. This bonus to damage is increased by half (+50%) if you are making an attack with a two-handed weapon, a one handed weapon using two hands, or a primary natural weapon that adds 1-1/2 times your Strength modifier on damage rolls. This bonus to damage is halved (–50%) if you are making an attack with an off-hand weapon or secondary natural weapon. When your base attack bonus reaches +4, and every 4 points thereafter, the penalty increases by –1 and the bonus to damage increases by +2. You must choose to use this feat before making an attack roll, and its effects last until your next turn. The bonus damage does not apply to touch attacks or effects that do not deal hit point damage.