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elena-s [515]
3 years ago
14

Can someone help me with this fast please? Thank You

Mathematics
1 answer:
egoroff_w [7]3 years ago
6 0
The answer is 3/10


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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
eduard

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}

7 0
3 years ago
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