I have heavy household outdoor wire, the grayish type meant to be burried, it has been hanging from the trees for about 8-9yrs now and is just fine. I think this is a 12/3 if I remeber correctly. Most likely the same thing you have.

My power pole is about 100' away from the first trailerhouse I had here and this cable in the trees ran from that pole to the shed by the house. I then went from an outlet in the shed to other stuff like the trailerhouse and a tree on the other side where I had a 4'X 4'x8' box I raised day old chicks in as a brooder till ready to be moved to the normal pen. This cable as I say is still working just fine tossed up in the trees over head. I don't do much down there now, but when I do and need power this is what I use for 120VAC to the trailer house still. Basically it's just a long extension cord and I never have ran much off it other than lights, vacume cleaners, stereo, saws, drills, ect... All low amp stuff only a few things at a time, and I never have problems, even when we lived in the trailer and used it this way.

As for burring a cable 18" deep, if you do that I would use some type of conduit or even plain PVC pipe at least. 18" is not very deep and it would be very easy to hit in the future if your doing any digging or driving any posts in that area later. Also rocks might cut through a bare cable as the ground shifts durring season changes.
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nothing to lose