Find a formula with dimensions

A small drop of water, knocked, wobbles. Its frequency $f$ might depend on the surface tension $\sigma$, the density $\rho$ and the radius $r$. You will make the program find the powers in $f = k\,\sigma^{a}\rho^{b}r^{c}$ by matching dimensions, with NumPy.

The idea. Each quantity is a list of powers of $(\text{M}, \text{L}, \text{T})$. Matching M, L and T on both sides gives three equations for $a$, $b$ and $c$.

Your tasks.

1. Write the dimensions of $\sigma$ (a force per length), $\rho$ and $r$.
2. Write the dimensions of a frequency.
3. Solve for the three powers.