How do you simplify #root3(-16x^8)#?

1 Answer

Answer:

#-2x^2root3(2x^2)#

Explanation:

We have:

#root3(-16x^8)#

I'm going to rewrite the terms under the root sign into terms of cubes:

#root3((-1)^3(2^3)2^1x^3x^3x^2)#

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:

#-1(2)(x)(x)root3(2^1x^2)#

and cleaning this up a bit:

#-2x^2root3(2x^2)#

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.