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

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