Always compare to the Normal line to see what the feat benefit is changing.
PRD wrote:
Benefit: While using this style, you gain a +2 bonus on saving throws against sleep effects, paralysis effects, and stunning effects. You ignore difficult terrain when you charge, run, or withdraw. You can also charge through squares that contain allies. Further, you can add 1-1/2 times your Strength bonus on the damage roll for your first unarmed strike on a given round.
Normal: You cannot charge or run through difficult terrain, and you cannot charge through a square that contains an ally. With an unarmed strike, you usually add your Strength bonus on damage rolls.
If it were just adding 1.5x Str on top of your normal bonus, that line in the Normal section would not be there because nothing is being changed; you'd be getting everything you used to, plus something more. Compare with Dragon Ferocity:
PRD wrote:
Benefit: While using Dragon Style, you gain a bonus on unarmed strike damage rolls equal to half your Strength bonus. 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.
There is no Normal line for Dragon Ferocity because nothing is being changed from defaults. You simply gain an additional, untyped bonus equal to half your Str bonus on all your Unarmed Strikes. So, with 4 Unarmed Strikes on your full-attack (presuming all are counted as main-hand), and both Dragon Style and Ferocity you'd have the following:
Attack 1) Dice + 1.5x Str + 0.5x Str + Other bonuses
Attack 2) Dice + 1.0x Str + 0.5x Str + Other bonuses
Attack 3) Dice + 1.0x Str + 0.5x Str + Other bonuses
Attack 4) Dice + 1.0x Str + 0.5x Str + Other bonuses
