Question

Which expression is equivalent to 4 sqrt 24x^6y/128x^4y^5

Answer 1

Here you go, I used a different site

Answer 2

Given expression: $\sqrt[4]{\frac{24x^6y}{128x^4y^5} }$.

$\mathrm{Cancel\:the\:common\:factor:}\:8$

$=\frac{3x^6y}{16x^4y^5}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}$

$\frac{x^6}{x^4}=x^{6-4}=x^2$

$=\frac{3x^2y}{16y^5}$

$\mathrm{Cancel\:the\:common\:factor:}\:y$

$=\frac{3x^2}{16y^4}$

$=\sqrt[4]{\frac{3x^2}{16y^4}}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

$=\frac{\sqrt[4]{3x^2}}{\sqrt[4]{16y^4}}$

$=\frac{\sqrt[4]{3x^2}}{\sqrt[4]{16}\sqrt[4]{y^4}}$

$=\frac{\sqrt[4]{3}\sqrt[4]{x^2}}{\sqrt[4]{16}\sqrt[4]{y^4}}$

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

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

Therefore, correct option is 4th option $\frac{\sqrt[4]{3x^2}}{2y}$.