what is the simplified form of the following expression?\n\\(sqrt3{\frac{4x}{5}}\\)\n\\(\frac{sqrt3{4x}}{5}\\…

Explanation:

Step1: Apply cube - root rule

We know that $\sqrt[3]{\frac{a}{b}}=\frac{\sqrt[3]{a}}{\sqrt[3]{b}}$, so $\sqrt[3]{\frac{4x}{5}}=\frac{\sqrt[3]{4x}}{\sqrt[3]{5}}$. To rationalize the denominator, we multiply the numerator and denominator by $\sqrt[3]{5^2}=\sqrt[3]{25}$.

Step2: Multiply numerator and denominator

$\frac{\sqrt[3]{4x}}{\sqrt[3]{5}}\times\frac{\sqrt[3]{25}}{\sqrt[3]{25}}=\frac{\sqrt[3]{4x\times25}}{\sqrt[3]{5\times25}}=\frac{\sqrt[3]{100x}}{\sqrt[3]{125}}$.

Step3: Simplify the denominator

Since $\sqrt[3]{125} = 5$, the simplified form is $\frac{\sqrt[3]{100x}}{5}$.

Answer:

$\frac{\sqrt[3]{100x}}{5}$