1 Answer

Swithin · Answer 1 · 2019-03-02T10:07:49+0000

To simplify

$\sqrt[4]{(24x^6y)/(128x^4y^5)}$

we need to use the fact that

$\sqrt[4]{x^4}=|x|$

Why the absolute value? It's because
(-x)^4=(-1)^4x^4=x^4 .

We start by rewriting as

$\sqrt[4]{(2^23x^6y)/(2^6x^4y^5)}$

$\sqrt[4]{(2^23x^4x^2y)/(2^42^2x^4y^4y)}$

Since
$x\\eq0$ , we have
$\frac xx=1$ , and the above reduces to

$\sqrt[4]{(3x^2y)/(2^4y^4y)}$

Then we pull out any 4th powers under the radical, and simplify everything we can:

$\frac1{\sqrt[4]{2^4y^4}}\sqrt[4]{(3x^2y)/(y)}$

$\frac1\sqrt[4]{3x^2}$

where
y>0 allows us to write
$\frac yy=1$ , and this also means that
|y|=y . So we end up with

$\frac{\sqrt[4]{3x^2}}{2y}$

making the last option the correct answer.

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