I have a question here requiring logical equivalences.

Express (not(p v q)) ^ r in disjunctive normal form by applying logical equivalences.

I must use logical equivalences to complete it, I cant construct a truth table.

from the laws i know associativity says ((p v q) v r) <==> (p v (q v r)).

and with distributivity i have (p v (q ^ r) <==> ((p v q) ^ (p v r))

I feel like these are the laws I need to solve the problem but I just cannot seem to wrap my head around it. Can somebody please put me on the right track. Thanks.