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.