Question 178163
{{{root(3,16x^4y^3)*root(3,12x^2y^4)}}} Start with the given expression



{{{root(3,16x^4y^3*12x^2y^4)}}} Combine the radicals



{{{root(3,192x^6y^7)}}} Multiply



{{{root(3,64*3*x^3*x^3*y^3*y^3*y)}}} Factor each term where at least one term is a perfect cube.



{{{root(3,64)*root(3,3)*root(3,x^3)*root(3,x^3)*root(3,y^3)*root(3,y^3)*root(3,y)}}} Break up the cube root.



{{{4*root(3,3)*x*x*y*y*root(3,y)}}} Take the cube root of 64 to get 4. Take the cube root of {{{x^3}}} to get "x". Take the cube root of {{{y^3}}} to get "y".



{{{4x^2*y^2*root(3,3y)}}} Rearrange the terms and multiply.



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Answer:



So {{{root(3,16x^4y^3)*root(3,12x^2y^4)=4x^2*y^2*root(3,3y)}}}