What is the simplified form of the following expression? assume and

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 514 People

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)

Answered by maham237 @ 25/12/2020

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:

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

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