Write in Exponential Form ( cube root of x square root of y)/( fourth root of xy^2)

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

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

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

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x y^{\frac{1}{2}}}$ as ${(x y^{\frac{1}{2}})}^{\frac{1}{3}}$ .

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

Step 3

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x y^{2}}$ as ${(x y^{2})}^{\frac{1}{4}}$ .

$\frac{{(x y^{\frac{1}{2}})}^{\frac{1}{3}}}{{(x y^{2})}^{\frac{1}{4}}}$