expression
without even asking; without even listening; without careful inquiry
Fixed expression meaning 'without so much as asking/listening/inquiring'. Often used to criticize someone who acts without gathering information or paying attention.
彼は聞きもしないで、私の意見を否定した。
He rejected my opinion without even asking.
聞きもしないで決めつけるのはよくない。
It's not good to jump to conclusions without even listening.
聞かずに is a simpler 'without asking/listening', while 聞きもしないで adds emphasis ('without even...').
Formed from the verb 聞く (to hear/ask) in its continuative form 聞き, plus the emphatic particle も, the negative しない, and the conjunctive particle で, literally 'without even doing the action of hearing/asking'.