What is the correct singular possessive form of brother-in-law? What is the correct plural possessive form?

Hint: A compound noun is one that has multiple terms in it. The most common combinations for compound nouns are [may be a noun + noun] and [could be an adjective + noun], but note that there are others. To find out the possessive form for any given compound noun we can add an apostrophe and an ‘s’ to the end of the noun just like how it is done for regular singular nouns. In a similar way to find the plural possessive form we may convert the base noun into the plural form then do just like in singular possessive form.

Complete answer:
 A compound noun is that which has multiple terms in it. The most common combinations for compound nouns are [may be a noun + noun] and [could be an adjective + noun], but note that there are others.
Here we are asked to find both singular and plural possessive forms so let us go about them one by one;
Remember that to find out the possessive form for any given compound noun we can add an apostrophe and an ‘s’ to the end of the noun just like how it is done for regular singular nouns.

The given compound noun is ‘brother-in-law’.
Now since the given word is in singular, we just need to append to the end of the given compound noun an apostrophe and s (‘s).
So the singular possessive form is; brother-in-law’s.

Then when we look at the way to find the plural possessive form, we may just need to convert the base noun into its plural form then go about the same procedure we use for singular possessive, that is adding an apostrophe and ‘s’ at the end.
Firstly make the base noun plural like this;
Brothers-in-law
Now we can just add an apostrophe and ‘s’ to the end of the compound noun.
So the plural possessive will look like this;
Brothers-in-law’s.
Take note that we rarely utilize this in a regular sentence, we would rather use other terms to convey the meaning.

Therefore the Singular possessive form is: brother-in-law’s and the Plural possessive form is: brothers-in-law’s.

Note: Remember that whenever we use a compound noun in a sentence, if we need to make it possessive we treat it as a single whole, meaning as one unit. So even if we are writing the possessive form we just need to add the ending (‘s) to the end of the compound noun. Similar thing has been done above, it may not sound sensible but it is grammatically correct.