Suppose a star has the same luminosity as our sun (3.8*1026watts) but is located at a distance of 10 light-years. what is its apparent brightness?

One light year is equal to 9.46*10^15 m. The star is 10 light years away, which is the same as 9.46*10^16 meters. The equation that relates brightness to distance and luminosity (in watts) is brightness = Luminosity / (4*pi*distance^2). The sun has a luminosity of 3.8*10^26 watts (NOT 3.8*1026 watts, as indicated in the problem statement). Using the given distance with the actual implied luminosity of the star: Brightness = 2.8*10^26 / (4*3.14159 * (9.46*10^16) ^2) = 2.49 e-9 W/m^2