Question 408332
Please don't use "x" for multiplication. Use the word "times" or use "*" (Shift+8).<br>
{{{root(3, x^2y^4) * root(3, x^4y^10)}}}
Your answer, {{{x^2*root(3, y^10)}}} is correct so far but it is unfinished. There is more simplifying we can do with the remaining cube root.<br>
{{{y^10}}} is not a perfect cube. (Variables are perfect cubes if their exponents are multiples of 3.) But it does have perfect cube factors. Factoring the  {{{y^10}}} into as many perfect cube factors as possible we get:
{{{x^2*root(3, y^3*y^3*y^3*y)}}}
Now we can use a property of radicals, {{{root(a, p*q) = root(a, p)*root(a, q)}}} to separate the factors inside the cube root into separate cube roots:
{{{x^2*root(3, y^3)*root(3, y^3)*root(3, y^3)*root(3, y)}}}
The cube roots of the perfect cubes will simplify:
{{{x^2*y*y*y*root(3, y)}}}
which simplifies to:
{{{x^2*y^3*root(3, y)}}}
This is the fully simplified expression.