Dimensional alalysis to show functional dependence

[General_Sax]

Homework Statement

Use the method of dimensional analysis to show that the functional dependence in equation (1) can be derived from an observational expression: lambda = k*mu*f^m*T^n.

Homework Equations

lambda=k\sqrt {{\frac {T}{\mu}}}{f}^{-1} (1)
lambda = k*mu*f^m*T^n
\mu={\frac {{\it kg}}{m}}
T={\frac {{\it kg}\,m}{{s}^{2}}}

The Attempt at a Solution

First I solve for n.

m={\frac {{m}^{n}}{m}}
n = 2

Now I solve for m.

0=0={1/s}^{m}{s}^{-2\,n}
m = -4

so now I have:

\lambda={\frac {ku{T}^{2}}{{f}^{-4}}}

I don't understand what the question means by "show that the functional dependence in equation (1). . ."

In equation (1) we were told that \lambda and T were variables. Well in equation I've derived \lambda and T could very well be variables, but I don't think I understand the question. But, if the question is asking me to equate the two expressions and prove an "identity", then I can't do that. Any help welcomed and appreciated.

When I try to "work" the units out they don't work out at all.

 

[General_Sax]

I tried to make it all pretty with the LaTeX, but it didn't work :(

 

[General_Sax]

Misread question. I thought the u had an exponent of 1, but it had an exponent of L.