Question 373073
{{{root(3, 128x^5y^4z^3)}}}
To simplify a cube root, look for perfect cube factors:
{{{root(3, 64*2*x^3*x^2*y^3*y*z^3)}}}
Then we use a property of radicals, {{{root(a, p*q) = root(a, p) * root(a, q)}}}, to separate the perfect cube factors into their own cube roots. (We will just leave all the factors which are not perfect cubes in a single cube root.):
{{{root(3, 64)*root(3, x^3)*root(3, y^3)*root(3, z^3)*root(3, 2*x^2*y)}}}
The cube roots of each of the perfect cubes can be simplified:
{{{4*x*y*z*root(3, 2x^2y)}}}
or
{{{4xyz*root(3, 2x^2y)}}}
This is the simplified version of your original expression.