You have an incorrect understanding of how these work together.
Let's run through how these would function on a level 8 unchained monk with 18 strength. Since you have 18 str, you get a +4 bonus to damage by base.
Next, Power Attack says:
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.
Since you're a level 8 unchained monk, you have 8 BAB, this means that Power Attack adds +6 damage by base, if this meets the italicized requirements, this damage bonus is boosted to a +9. Running through the list of possibilities we see:
- Two-Handed Weapon: Nope, Unarmed strikes do not meet this option as per their rules.
An unarmed strike is always considered a light weapon.
- One-handed weapon wielded in two hands: Nope, Unarmed Strikes are considered a light weapon as per the quote above.
Primary Natural Attack: Well, if we look at Unchained Monk we see:
A monk’s unarmed strike is treated as both a manufactured weapon and a natural weapon for the purpose of spells and effects that enhance or improve either manufactured weapons or natural weapons.
However, the ability does not designate that they are treated as a Primary natural weapon, just that they are treated as a natural weapon. This means they do not qualify for the extra 50% damage, and only a receive a +6 bonus.
Finally, let's look at Dragon Ferocity:
While using Dragon Style, increase your Strength bonus on unarmed strike damage rolls by an additional one-half your Strength bonus, to a total of double your Strength bonus on the first attack and 1-1/2 times your Strength bonus on the other attacks. When you score a critical hit or a successful Stunning Fist attempt against an opponent while using this style, that opponent is also shaken for a number of rounds equal to 1d4 + your Strength bonus.
This means you'd double your strength bonus on your first attack, giving you an additional +4 damage on the attack. On successive attacks, this is lowered to a 50% bonus, resulting in only an additional +2 damage on the attack. Note that Dragon Ferocity only increases the bonus damage from strength, not anything else like Power Attack.
Overall, this works out to be a total of +14 damage (+4 strength, +6 Power Attack, +4 Dragon Ferocity) on the first attack, and +12 damage (+4 strength, +6 Power Attack, +2 Dragon Ferocity) on successive ones.