Since we have a cubic root, we're interested in factoring cubes inside the root, so that we can take them out. If we factor 648, we have
[tex]648=2^3\times 3^4=2^3\times 3^3\times 3 = (2\times 3)^3\times 3 = 3\times 6^3[/tex]
So, we have
[tex]3x\sqrt[3]{648 x^4 y^8} = \sqrt[3]{3\times 6^3\cdot x^3\cdot x \cdot y^6\cdot y^2}=3x\cdot 6\cdot x\cdot y^2\sqrt[3]{3\cdot x\cdot y^2}[/tex]
And the result simplifies to
[tex]18x^2y^2\sqrt[3]{3xy^2}[/tex]
