Question

If two stars differ by 9.6 magnitudes what is their flux ratio?

Answer 1

Borrowing from the tradition of the ancient Greeks, the first ones
who tried to describe the brightness of stars with numbers ...

                        6 magnitudes  =  a ratio of 100 .

In more modern notation . . .

                       1 magnitude = ratio of    (100) ^ (1/6)

                                             =  about  2.154...

                 9.6 magnitudes  =  (100) ^ (9.6/6) 

                                             =  100¹·⁶ 

                                             =   1,584.89  (rounded)