the exploit is done running a Linux kernel module , PS3-slim doesnt have the option Other OS in the menu like the big PS3 , so you cannot install Linux in PS3 Slim to run the kernel.
right now the exploit is crap , only bypasses lvl1 security , you still need the master key that is in one of the SPU's without that the PS3 is not hacked , you just have access to memory in Other OS mode and not in Game mode.