Write the Fraction in Simplest Form cube root of 6* square root of 6

$\sqrt[3]{6} \cdot \sqrt{6}$

Multiply $\sqrt[3]{6} \sqrt{6}$ .

Rewrite the expression using the least common index of $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{6}$ as $6^{\frac{1}{3}}$ .

$6^{\frac{1}{3}} \sqrt{6}$

Rewrite $6^{\frac{1}{3}}$ as $6^{\frac{2}{6}}$ .

$6^{\frac{2}{6}} \sqrt{6}$

Rewrite $6^{\frac{2}{6}}$ as $\sqrt[6]{6^{2}}$ .

$\sqrt[6]{6^{2}} \sqrt{6}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\sqrt[6]{6^{2}} \cdot 6^{\frac{1}{2}}$

Rewrite $6^{\frac{1}{2}}$ as $6^{\frac{3}{6}}$ .

$\sqrt[6]{6^{2}} \cdot 6^{\frac{3}{6}}$

Rewrite $6^{\frac{3}{6}}$ as $\sqrt[6]{6^{3}}$ .

$\sqrt[6]{6^{2}} \sqrt[6]{6^{3}}$

Combine using the product rule for radicals.

$\sqrt[6]{6^{2} \cdot 6^{3}}$

Multiply $6^{2}$ by $6^{3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[6]{6^{2 + 3}}$

Add $2$ and $3$ .

$\sqrt[6]{6^{5}}$

Raise $6$ to the power of $5$ .

$\sqrt[6]{7776}$