Simplify the Radical Expression sixth root of 6* cube root of 6^2

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

Raise $6$ to the power of $2$ .

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

Multiply $\sqrt[6]{6} \sqrt[3]{36}$ .

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{36}$ as $36^{\frac{1}{3}}$ .

$\sqrt[6]{6} \cdot 36^{\frac{1}{3}}$

Rewrite $36^{\frac{1}{3}}$ as $36^{\frac{2}{6}}$ .

$\sqrt[6]{6} \cdot 36^{\frac{2}{6}}$

Rewrite $36^{\frac{2}{6}}$ as $\sqrt[6]{36^{2}}$ .

$\sqrt[6]{6} \sqrt[6]{36^{2}}$

Combine using the product rule for radicals.

$\sqrt[6]{6 \cdot 36^{2}}$

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

$\sqrt[6]{6 \cdot {(6^{2})}^{2}}$

Multiply the exponents in ${(6^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $2$ by $2$ .

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

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

$\sqrt[6]{6^{1 + 4}}$

Add $1$ and $4$ .

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

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:

$4.45101825 \dots$