Simplify fourth root of 36* cube root of 6

$\sqrt[4]{36} \cdot \sqrt[3]{6}$

Rewrite $36$ as $6^{2}$ .

$\sqrt[4]{6^{2}} \cdot \sqrt[3]{6}$

Rewrite $\sqrt[4]{6^{2}}$ as $\sqrt{\sqrt{6^{2}}}$ .

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

Pull terms out from under the radical, assuming positive real numbers.

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

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

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

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

$6^{\frac{1}{2}} \sqrt[3]{6}$

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

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

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

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

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

$\sqrt[6]{6^{3}} \cdot 6^{\frac{1}{3}}$

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

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

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

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

Combine using the product rule for radicals.

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

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

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

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

Add $3$ and $2$ .

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

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

$\sqrt[6]{7776}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt[6]{7776}$

Decimal Form:

$4.45101825 \dots$