Answer:
(E) [tex]\frac{\sqrt[3]{6x^2y^2}}{2y}[/tex]
Step-by-step explanation:
The given expression is:
[tex]\sqrt[3]{\frac{12x^2}{16y}}[/tex]
Upon solving the above expression, we have
=[tex]\sqrt[3]{\frac{3x^2}{4y}}[/tex]
=[tex]\frac{\sqrt[3]{3x^2}}{\sqrt[3]{4y}}[/tex]
Now, multiplying and dividing by [tex]\sqrt[3]{(4y)^2}[/tex], we have
=[tex]\frac{\sqrt[3]{3x^2}}{\sqrt[3]{4y}}{\times}\frac{\sqrt[3]{(4y)^2}}{\sqrt[3]{(4y)^2}}[/tex]
=[tex]\frac{\sqrt[3]{48x^2y^2}}{\sqrt[3]{64y^3}}[/tex]
=[tex]\frac{2\sqrt[3]{6x^2y^2}}{4y}[/tex]
=[tex]\frac{\sqrt[3]{6x^2y^2}}{2y}[/tex]
which is the required simplified form of the above given expression.
Thus, option (E) is correct.
