How do you simplify #root3(-16x^8)#?
I'm going to rewrite the terms under the root sign into terms of cubes:
The cube root and the cubes inside the root are inverse functions, so we simply end up with the base term. Everything else is a "remainder" and stays within the root sign:
and cleaning this up a bit:
While there is the same term inside as outside the root sign, we can't really factor it more than where we are, so I'll leave it here.