how we caclulate x1.5

[With a box]

let's say I cast empowered fireball at CL 10, then its damege roll is 10d6+5d6 or (10d6)X(1.5)?
those two mathodes make different result due to having different deviation.

[Troacctid]

It's the second one, as stated in the feat description.


All variable, numeric effects of an empowered spell are increased by one-half. An empowered spell deals half again as much damage as normal, cures half again as many hit points, affects half again as many targets, and so forth, as appropriate. For example, an empowered magic missile deals 1-1/2 times its normal damage (roll 1d4+1 and multiply the result by 1-1/2 for each missile).

[Khedrac]

It's also worth noting that an empowered, maximised fireball does "60 + 0·5×(10d6)" damage, not "90" nor "60 + 5d6" (it's a flatter probability distribution).