"An hour's work" and "a two weeks' holiday". In "an hour's work" does the indefinite article belong to the noun "work"? As far as I know, "work" is an uncountable noun. In "a two week's holiday" does the article belong to "holiday"? Is it better to say "He took a two weeks' holiday" or "He took two weeks' holiday"? I know not everyone likes the expression "an hour's work" but I took it from a textbook which has been reliable so far. Is "It was a one-hour's work" correct? If yes, why?
No - the article belongs to the hour.
The indefinite article "a" can usually be substituted by the number 1:
- an apple
- one apple
- I have a child
- I have one child
That's why in your second example of "two week's holiday" there is no article, because the number takes its place. I'm sure you understand that this example refers to one holiday that is two weeks in length, not two holidays lasting a week each.
The reason you can use "An hour's work" is because, the "an" refers to "hour", not "work". The second example "two weeks' holiday", has no article, since "a" is the same as "one", thus we can't say "one two weeks' holiday".
P.S. However, if you really want to add an article before the second example, you can't change it into "a two-week holiday". If you want to know the reason, you can tell me in the comments.