'I don't give a rats ass' is a similar phrase to 'I don't give a shit'.This basicaly means that the person who uses these words doesn't care about the circumstance whatsover.Literally,it means the person doesn't care about that situation even to the extent of a rats ass!
Simular to the phrase "I dont give a rats ass" but for use in enviroments with under 3's. If you want to say "I dont give a rats ass" but happen to be in the crèche you can alternatively use "I dont give a rats left foot".
This phrase is also good around people that would willingly class themselves as snowflakes, assholes or English language Nazi's.