Simplify fourth root of 6* cube root of 6^2

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

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

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

Multiply $\sqrt[4]{6} \sqrt[3]{36}$ .

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{6}$ as $6^{\frac{1}{4}}$ .

$6^{\frac{1}{4}} \sqrt[3]{36}$

Rewrite $6^{\frac{1}{4}}$ as $6^{\frac{3}{12}}$ .

$6^{\frac{3}{12}} \sqrt[3]{36}$

Rewrite $6^{\frac{3}{12}}$ as $\sqrt[12]{6^{3}}$ .

$\sqrt[12]{6^{3}} \sqrt[3]{36}$

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

$\sqrt[12]{6^{3}} \cdot 36^{\frac{1}{3}}$

Rewrite $36^{\frac{1}{3}}$ as $36^{\frac{4}{12}}$ .

$\sqrt[12]{6^{3}} \cdot 36^{\frac{4}{12}}$

Rewrite $36^{\frac{4}{12}}$ as $\sqrt[12]{36^{4}}$ .

$\sqrt[12]{6^{3}} \sqrt[12]{36^{4}}$

Combine using the product rule for radicals.

$\sqrt[12]{6^{3} \cdot 36^{4}}$

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

$\sqrt[12]{6^{3} \cdot {(6^{2})}^{4}}$

Multiply the exponents in ${(6^{2})}^{4}$ .

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

$\sqrt[12]{6^{3} \cdot 6^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\sqrt[12]{6^{3} \cdot 6^{8}}$

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

$\sqrt[12]{6^{3 + 8}}$

Add $3$ and $8$ .

$\sqrt[12]{6^{11}}$

Raise $6$ to the power of $11$ .

$\sqrt[12]{362797056}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt[12]{362797056}$

Decimal Form:

$5.16779542 \dots$