Purrrrfection skill clarification

So IF I was to use Fire Bomb(90 Power) with Purrfection. It would only have 45 Power because of the 50% decrease in using a skill that's not the same element as the monster. But with Yoga on it would basically do normal damage?

Yeah basically ^^

No that isn't how it works. STAB bonus would be added to the final damage output not the Power. A moves Power is used with an attacking monsters ATK/MATK to calculate the base damage, that base damage is modified by STAB's 50% boost, a Critical Hit's 100% boost, and any offensive Talents and the 0.5x, 1x or 2x element modifiers. This final damage output is then lowered by the defending monsters DEF/MDEF and any defensive talents it has.

If you had Fire Blast on a Flight, Yoga Purrection and Blaze and the damage output for the Flight was 100 damage, the Blaze would do 150 damage with STAB and the Yoga Purr would do 200 damage.

The Blaze could benefit from weather that can increase the power by 50% and Adaptibility which adds ~40% to the final damage thereby out damaging the Yoga Purr by a significant margin if they both used Fire Blast (if you ignore stats entirely). But the Flight and especially the Yoga Purr benefit by being able to use many different elements.

There has to be something wrong then... My earlier experiment where my yoga perfffection and blaze stats were almost alike, my blaze still did more damage with no adapatabilty power

Purrfection is <3