Empowered Fireball + Amulet of the Spirits (Flame)

Rules Questions

I just want to make sure I understand this correctly.

If a 10th level wizard wearing an Amulet of the Spirits (Flame) uses a swift action to make one target vulnerable to fire, and then casts an empowered fireball at that target, how much damage does it take?

I'm thinking it would be (10d6 x 1.5) x 1.5.

If the wizard has the evocation spell school, since than power is not multiplied for evocation, it would be ((10d6 x 1.5)+5) x 1.5

Lastly if this is an evocation wizard10/crossblooded sorcerer(dragon/orc) it should look like (((10d6+20) x 1.5)+5) x 1.5

Is all that correct? sorry for the convoluted question.

Seems legit to me.


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