An anti-matter bomb which humans have, could fit in a humans hand, and be bigger than the predators self destruct. The biggest bomb made by Humans was 58 million tons of TNT http://en.wikipedia.org/wiki/Tsar_Bomba
Now an anti matter bomb that fits in your hand would be bigger than that. But an antimatter bomb that was the size of the tsar, that is a multi-stage annihilation fusion bomb, would be a billion tons of TNT.
http://sfgate.com/cgi-bin/article.cgi?file=/c/a/2004/10/04/MNGM393GPK1.DTL
Now say humans had this bomb, which is very possible, they could and would annihilate the predators home world with a giant multi-stage annihilation, fusion, annihilation ionized helium bomb!
And humans could probably make even bigger bombs, with a four stage anti-matter bomb, and so on.
And just so you know you can't have a four stage, because you can't end in fusion, only in fission and annihilation. So an 11 stage antimatter bomb should destroy the predator's home world.
in space...
no one...
can hear you scream...