Dimensional Analysis? Getting funny answers here

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SUMMARY

The discussion focuses on the dimensional analysis of the formula for the radius of a shell, defined as R[shell] = ((Luminosity*time^3)/(density))^1/5. Participants emphasize the importance of breaking down quantities into their fundamental units to verify the dimensional consistency of the equation. The original poster encounters discrepancies in their calculations, specifically obtaining powers of 1/3 instead of the expected 1/5. Community members stress the necessity of sharing detailed work to identify errors in the analysis.

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  • Basic knowledge of mathematical exponents
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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?
 
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