which expression is equivalent to 4√24x∧6y÷ 128x∧4y∧5

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.

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