Personaly I would not do it. Although I see no safety problems doing so. If It were me I would buy some large enough tubbing to put it in. So nothing could go wrong. Like running over something that could cut the wire.
A lot of cars have coolant hoses and A/C lines under the car, I would still put it in some corregated tubing to deflect any debris though. To me the real issue is getting it back into the car without causing a water leak in your trunk.
I did it, but I slid the wire through a flexible conduit tubing first to protect from harsh condiditons. Bought a 25' roll at Home Depot for a few dollars.
i was loosing a lot of power trying to push my kenwood at 1 ohm and i put a battery out of an suv in the trunk i put it inside a cooler and strapped it down is that safe
depends on the battery- they give off hydrogen gas as they discharge, so that can possibly accumulate in the cooler and go boom with a spark......hard to say- sounds sketchy to me...
Ive run mine under my truck for the past 2 years with no conduit. Its secured every 5 0r so inches to the inside of the frame with wire clips. No problems so far