Mathematics: Which expression is equivalent to 4√24x∧6y÷ 128x∧4y∧5

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

emurray

04.01.2022

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

Step-by-step explanation:

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

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

= $\sqrt[4]{(\frac{3}{16})\times {(x)^{6-4}}\times{(y)^{1-5}}}$

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

= $\sqrt[4]{\frac{3}{(2)^{4}}\times x\times y^{-4}}$

= $\sqrt[4]{(3\times x^{2)\times (\frac{y^{-1}}{2})^{4}}}$

= $\frac{y^{-1}}{2}\sqrt[4]{3x^{2}}$

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

Option D. $\sqrt[4]{\frac{3x^{2}}{2y}}$ is the correct answer.

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