Question

what is the simplified form of the following expression? Assume X 0 and y 0. 2(^4 sqrt 16 x) -2(^4 sqrt 2y )+3 (^4 sqrt 81x ) -4 ( ^4 sqrt 32y)

Answer 1

Answer is C

Just took the test.

Answer 2

For this case we have the following expression:

`2(\sqrt[4]{16x})-2(\sqrt[4]{2y})+3(\sqrt[4]{81x})-4(\sqrt[4]{32y})`

Rewriting the numbers within the roots we have:

`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})`

Then, by properties of powers we have:

`2(\sqrt[4]{2^4x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3^4x})-4(\sqrt[4]{2^42y})`

Then, by radical properties we have:

`2(2\sqrt[4]{x})-2(\sqrt[4]{2y})+3(3\sqrt[4]{x})-4(2\sqrt[4]{2y})`

Rewriting the expression we have:

`4\sqrt[4]{x}-2\sqrt[4]{2y}+9\sqrt[4]{x}-8\sqrt[4]{2y}`

Finally, adding similar terms we have:

`(4+9)\sqrt[4]{x}-(2+8)\sqrt[4]{2y}`

`13\sqrt[4]{x}-10\sqrt[4]{2y}`

Answer:

The simplified form of the expression is:

`13\sqrt[4]{x}-10\sqrt[4]{2y}`