Star x has a magnitude of 13. star y has a magnitude of 10. the brightness is?

You don't mention if you want the ratio X:Y or Y:X.

Apparent magnitude was originally based on how bright something appeared to the eye such that a star that is half as bright had one higher magnitude. The visible stars were divided into magnitudes 1 to 6 with the brightest being 1 and the dimmest being 6. This was later formalized into a more scientific definition where a magnitude 1 star was said to be 100x brighter than a magnitude 6 stars. Thus a change of 5 magnitudes represents 100 times difference in brightness or a change of one magnitude is a change in brightness by a factor of the fifth root of 100. This fifth root of 100 is called Pogson's ratio. It is approximately 2.51. So a change in magnitude from 10 to 13 means it is three orders of magnitude dimmer and therefore 1/2.51^3 = 1/15.8th as bright.

So your answer is either 15.8 : 1 or 1 : 15.8 depending on whether you want the ratio of y : x or x : y.

Note star x is the one that is 15.8 times dimmer than star y.