Answer:
Option D. [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex]
Step-by-step explanation:
[tex]\sqrt[4]{\frac{24x^{6}y}{128x^{4}y^{5}}}[/tex]
[tex]\sqrt[4]{(\frac{24}{128})\times (\frac{x^{6}}{x^{4}})\times (\frac{y}{y^{5}})}[/tex]
= [tex]\sqrt[4]{(\frac{3}{16})\times {(x)^{6-4}}\times{(y)^{1-5}}}[/tex]
= [tex]\sqrt[4]{(\frac{3}{16})\times x^{2}y^{-4}}[/tex]
= [tex]\sqrt[4]{\frac{3}{(2)^{4}}\times x\times y^{-4}}[/tex]
= [tex]\sqrt[4]{(3\times x^{2)\times (\frac{y^{-1}}{2})^{4}}}[/tex]
= [tex]\frac{y^{-1}}{2}\sqrt[4]{3x^{2}}[/tex]
= [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex]
Option D. [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex] is the correct answer.
