Question 203101
{{{root(3,(108x^3y^7)/(2y^3))}}} Start with the given expression.



{{{root(3,(54x^3y^7)/(y^3))}}} Reduce the coefficients.



{{{root(3,54x^3y^(7-3))}}} Divide the common variable terms by subtracting the exponents.



{{{root(3,54x^3y^4)}}} Subtract



{{{root(3,27*2x^3y^4)}}} Factor 54 into 27*2



{{{root(3,27*2x^3y^3*y)}}} Factor {{{y^4}}} into {{{y^3*y}}}



{{{root(3,27)*root(3,2)*root(3,x^3)*root(3,y^3)*root(3,y)}}} Break up the root.



{{{3*root(3,2)*root(3,x^3)*root(3,y^3)*root(3,y)}}} Take the cube root of 27 to get 3



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



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



{{{3xy*root(3,2y)}}} Rearrange the terms and combine the roots.



So {{{root(3,(108x^3y^7)/(2y^3))=3xy*root(3,2y)}}} where {{{y<>0}}}