"Les robes des femmes"
it's all in the articles: they sound different. "Le" almost sounds like "luh" and "Les" sounds like "lay". that's how you know if it's plural or not.
I repeat: no "s" is to be heard. the plural forms which you should hear are "les" and "des". This sentence in the singular form is "la robe de la femme". Quite different!
There are lots of useful videos, concerning French pronunciation on youtube. Though as a very general rule, most constants at the end of the word in French are not pronounced, hence why you need to listen to the article to consider if it is plural or not. However I seriously recommend you look up French pronunciation, as it is quite different to English. This is a good comprehensive lesson on the subject: https://www.youtube.com/watch?v=ckzM6-Ee7wU
The only way one knows is in the correct pronunciation of les and des. The s' are not pronounced. Les and des are both pronounced differently than le and de. Check that out and you should be able to discern the difference.
I understand you don't always hear plurals, but how am I to distinguish this between "The woman's dress" without context?
"Le robe de femme"
It would not be "Le robe", because "robe" is feminine. It would be "La robe", which sounds quite different than "Les robes".
If it were a masculine noun, you can tell the difference between "Le" and "Les" because they sound different. See my other comment farther up to see what I'm talking about.
In singular it would be "LA robe DE LA femme" - so you must listen very carefully.
Le is pronounced slightly like "luh", whereas "les" is more of a "lay"
the exercise says "Les robes des femmes" and the solution given is "the dresses of the women" but what part of this implies ownership?
"des" literally means "of the". If you were to say, "the car of the man", another way of saying that is "the man's car." Therefore, "the dresses of the women" can also be written "the women's dresses."
What I don't understand is, why can't this be "les robes des femme", or "the woman's dresses"?
If you refer to several dresses owned by one woman: "les robes DE LA femme" = the woman's dresses If you refer to several dresses owned by several women: "les robes DES femmeS" (contraction of DE-LES) = the women's dresses".