Question 190602
{{{3*root(4,x^3y)+5*root(4,x^7y^5)}}} Start with the given expression.



{{{3*root(4,x^3y)+5*root(4,x^4*x^3y^4*y)}}} Factor {{{x^7y^5}}} to get {{{x^4*x^3y^4*y}}}



{{{3*root(4,x^3y)+5*root(4,x^4)*root(4,x^3)*root(4,y^4)*root(4,y)}}} Break up the root.



{{{3*root(4,x^3y)+5*x*root(4,x^3)*y*root(4,y)}}} Take the 4th root of {{{x^4}}} and {{{y^4}}} to get "x" and "y"



{{{3*root(4,x^3y)+5xy*root(4,x^3y)}}} Recombine the roots.



{{{(3+5xy)*root(4,x^3y)}}} Factor out the GCF {{{root(4,x^3y)}}}



So {{{3*root(4,x^3y)+5*root(4,x^7y^5)=(3+5xy)*root(4,x^3y)}}} where every variable is non-negative.