A particular star is 5.2*10^18 meters away from Earth and has a luminosity of 8.9*10^29 watts. Ignoring the effects of the atmosphere, what

I'm guessing here but

the lioght will spread out in a sphere

the surface area of a sphere is   4*pi*r^2

r=5.2*10^18

So the surface are of THIS sphere is 

$$\\SA=4*\pi*(5.2*10^{18})^2\\ SA=4*\pi*5.2^2*10^{36}\\$$

$${\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{5.2}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{\pi}} = {\mathtt{339.794\: \!661\: \!412\: \!272\: \!036\: \!7}}$$

$$\\SA= 3.39797946614122720367 * 10^{38}\;\; M^2\\\\ Brightness \approx 8.9*10^{29}/(3.39797946614122720367 * 10^{38}) \;\;$watts per square metre$\\\\ Brightness \approx 8.9*10^{-9}/(3.39797946614122720367 ) \;\;$watts per square metre$\\\\ Brightness \approx 2.62*10^{-9} \;\;$watts per square metre$\\\\$$

I got the same as anon so maybe we are both correct    

A particular star is 5.2*10^18 meters away from Earth and has a luminosity of 8.9*10^29 watts. Ignoring the effects of the atmosphere, what is the brightness of the star, in watts per square meter, as observed from earth?

Brightness=8.9*10^29 / 4 x Pi x (5.2*10^18)^2

=2.619 x 10^-9 W/M^2