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

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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