MHB Understanding Dimensional Analysis: Solving for i, j, and k Values

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The discussion focuses on deriving the values of "i, j, and k" in dimensional analysis. The key point is that when equating powers, the fundamental quantities of length and mass must have exponents of zero to isolate time with an exponent of one. This leads to the formulation of three equations with three unknowns, which can be solved simultaneously. Participants emphasize the importance of correctly setting up the equations based on dimensional consistency. Understanding this process is crucial for successfully applying dimensional analysis in problem-solving.
dexstarr
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I'm having trouble understanding a step. How are the values of " i , j , and k " derived? When equating the powers what step has to be done? I have been stumped on this for a while and I think I'm just over thinking it.

https://www.dropbox.com/s/agc0ga9hsjd04jn/Sample%20Problem.png
 

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What they have done is to use the fact that the fundamental quantities of length and mass must have exponents of zero, since we wish only to have a unit of time left, with an exponent of 1. So this gives us 3 equations in 3 unknowns.
 

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