I searched this forum and found similar problem:
And last part of last post:
If this is correct calculation for matching photoshop colors. Cod this as pure function in BP, and multiply RGB color values by result from it.
That power function has 2.4 so that may be usual gamma correction.
However if conversion is not linear you need to find formula or get somebody who can spot color differences (some pro artist).
ps.
I think this formula is accurate, there is post on stackoverflow explaining it with this same formula.