Simplify sixth root of x* fourth root of y^3

$\sqrt[6]{x} \cdot \sqrt[4]{y^{3}}$

Step 1

Rewrite the expression using the least common index of $12$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{x}$ as $x^{\frac{1}{6}}$ .

$x^{\frac{1}{6}} \sqrt[4]{y^{3}}$

Rewrite $x^{\frac{1}{6}}$ as $x^{\frac{2}{12}}$ .

$x^{\frac{2}{12}} \sqrt[4]{y^{3}}$

Rewrite $x^{\frac{2}{12}}$ as $\sqrt[12]{x^{2}}$ .

$\sqrt[12]{x^{2}} \sqrt[4]{y^{3}}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{y^{3}}$ as $y^{\frac{3}{4}}$ .

$\sqrt[12]{x^{2}} y^{\frac{3}{4}}$

Rewrite $y^{\frac{3}{4}}$ as $y^{\frac{9}{12}}$ .

$\sqrt[12]{x^{2}} y^{\frac{9}{12}}$

Rewrite $y^{\frac{9}{12}}$ as $\sqrt[12]{y^{9}}$ .

$\sqrt[12]{x^{2}} \sqrt[12]{y^{9}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[12]{x^{2} y^{9}}$