How to separate nested subexpressions to list?

Question

I have an expression like this:

3*Subscript[v, 0]^3*Subscript[v, 1]^8*Subscript[v, 2]^7*Subscript[v, 3]^2

I would like to extract the exponents and put them into a list sorted by the subscript and separate the constant factor. So I would like to have an output like this:

{3, {3,8,7,2}}

And in case the constant is missing in the expression, it should be output as 1, naturally. How can I achieve this? I tried sequence patter matching, but I did not succeed.

Answer 1

you can use

CoefficientRules

and get

{{3, 8, 7, 2} -> 3}

If we call your expression a then this should do the work

##&@@@CoefficientRules@a    

{{3, 8, 7, 2}, 3}

Answer 2

Try this (expr is your expression):

expr /. Times -> List /. {a_Integer, b__} :> {a, {b}}
MapAt[Total@Outer[Exponent, #, Array[Subscript[v, #] &, 4, 0]] &, %, 2]