Why do astronomers infer that the Sun's energy comes from nuclear fusion reactions...

c. Why do astronomers infer that the Sun's energy comes from nuclear fusion reactions?  How do we know it does not come from chemical burning?
d. Explain how the Sun produces energy by nuclear fusion.
e. When we look at stars in the sky we see a wide range of brightness.  Explain the factors that would make one star appear brighter than another.        

(Please explain in your own words, if possible)