For this case we have the following expression:
[tex]2(\sqrt[4]{16x})-2(\sqrt[4]{2y})+3(\sqrt[4]{81x})-4(\sqrt[4]{32y})[/tex]
Rewriting the numbers within the roots we have:
[tex]2(\sqrt[4]{2*2*2*2x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3*3*3*3x})-4(\sqrt[4]{2*2*2*2*2y})[/tex]
Then, by properties of powers we have:
[tex]2(\sqrt[4]{2^4x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3^4x})-4(\sqrt[4]{2^42y})[/tex]
Then, by radical properties we have:
[tex]2(2\sqrt[4]{x})-2(\sqrt[4]{2y})+3(3\sqrt[4]{x})-4(2\sqrt[4]{2y})[/tex]
Rewriting the expression we have:
[tex]4\sqrt[4]{x}-2\sqrt[4]{2y}+9\sqrt[4]{x}-8\sqrt[4]{2y}[/tex]
Finally, adding similar terms we have:
[tex](4+9)\sqrt[4]{x}-(2+8)\sqrt[4]{2y}[/tex]
[tex]13\sqrt[4]{x}-10\sqrt[4]{2y}[/tex]
Answer:
The simplified form of the expression is:
[tex]13\sqrt[4]{x}-10\sqrt[4]{2y}[/tex]
