Question

What is the simplified form of the following expression?


`2 (\sqrt[4]{16x}) - 2 (\sqrt[4]{2y} ) + 3 (\sqrt[4]{81x} ) - 4 (\sqrt[4]{32y} )`
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Answer 1

We have

`16=2^4\implies\sqrt[4]{16}=2`

`81=3^4\implies\sqrt[4]{81}=3`

`32=2^5\implies\sqrt[4]{32}=2\sqrt[4]{2}`

So

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

is equivalent to

`2^2\sqrt[4]{x}-2\sqrt[4]{2y}+3^2\sqrt[4]{x}-8\sqrt[4]{2y}`

which reduces to

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