In the ももたろう tale there's a sentence that goes like:
Which translates as
If the old man went to the mountain to cut trees
the old woman would go out to the river to wash clothes.
In the old woman's case the verb せんたく is presented in its dictionary form and is not modified by the particle に, which gives the sense of purpose (to go out to do something). So why the same is not true for the old man? Why 木を切りに instead of 木を切るに?