B Alpha Centauri has an apparent magnitude of -0.27, whereas the apparent
magnitude of Alpha Crucis is 0.77. Identify which star appears brighter when observed from
Earth. Explain your answer.

Alpha centauri will be brighter than Alpha Crucis .

Explanation:

Apparent magnitude of a star measures how bright a star is .

This scale is reverse logarithmic ie , the brighter  the  star , the lower is its magnitude . A magnitude equal to 5 scale higher represents less magnitude by a factor of 1/ 100 . In this way a difference of 1 magnitude represents a brightness ratio of 2.512 . Hence a star of brightness magnitude of 7 is less bright by a factor 2.512  than that of a star magnitude of 6 .