I typically have my students use the "factor-label" method. It's longer to write out but is the easiest way (in my opinion) to check your work.

We want to express kNm in terms of kNmm. We know that 1 m = 1000 mm. So:

Again use factor-label. We know that so there is no real conversion there. We also know that 10 mm = 1 cm. We have two of these, though, so the factor needs to be squared.

So

-Dan