Dimensional Analysis? Getting funny answers here

[lavenderblue]

This question is on the radius of a shell, which is:

R[shell] = ((Luminosity*time^3)/(density))^1/5

I have been asked to prove this using dimensional analysis, and have broken the quantities down into their basic units, but seem to be getting really funny answers (with most of the powers to 1/3). Can anyone help?

 

[D H]

We can't help you find your error if you don't show your work!