Question 193112
{{{root(3,432x^8)}}} Start with the given expression.



{{{root(3,216*2x^8)}}} Factor 432 into {{{216*2}}}. Note: 216 is a perfect cube



{{{root(3,216*2*x^3*x^3*x^2)}}} Factor {{{x^8}}} into {{{x^3*x^3*x^2}}}.



{{{root(3,216)*root(3,2)*root(3,x^3)*root(3,x^3)*root(3,x^2)}}} Break up the root.



{{{6*root(3,2)*root(3,x^3)*root(3,x^3)*root(3,x^2)}}} Take the cube root of 216 to get 6



{{{6*root(3,2)*x*x*root(3,x^2)}}} Take the cube root of {{{x^3}}} to get {{{x}}}



{{{6x^2*root(3,2x^2)}}} Rearrange the terms and multiply 



So {{{root(3,432x^8)=6x^2*root(3,2x^2)}}}