Wiktionary
gave a rat's ass
vb. (en-simple pastgive a rat's ass)
Usage examples of "gave a rat's ass".
Neither side gave a rat's ass about the welfare of the troops they'd hiredthe Skybolts were just so many warm, weapon-wielding bodies to them, and if they thought about it at all, they probably assumed that the Company members welcomed a certain number of losses, as it made for fewer to split the pay at the end.
Like many scientists, Gabe was oblivious to the fact that no one gave a rat's ass about research unless it could be expressed in terms of dollars.