Question

which of the following is equivalent to \\(\frac{x^{\frac{2}{3}}}{y^{-\frac{3}{4}}}\\)?

\\(\bigcirc\quad \sqrt{x^2} \cdot \sqrt3{y^4}\\)
\\(\bigcirc\quad \sqrt3{x^2} \cdot \sqrt4{y^3}\\)
\\(\bigcirc\quad \frac{\sqrt{x^3}}{\sqrt3{y^4}}\\)
\\(\bigcirc\quad \frac{\sqrt3{x^2}}{\sqrt4{y^3}}\\)

Explanation:

Step1: Rewrite negative exponent

$$\frac{x^{\frac{2}{3}}}{y^{-\frac{3}{4}}} = x^{\frac{2}{3}} \cdot y^{\frac{3}{4}}$$

Step2: Convert to radical form

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

Answer:

B. \(\sqrt[3]{x^2} \cdot \sqrt[4]{y^3}\)