Simplify ( fourth root of 36* fourth root of 216)/( fourth root of 6)

$\frac{\sqrt[4]{36} \cdot \sqrt[4]{216}}{\sqrt[4]{6}}$

Combine $\sqrt[4]{36}$ and $\sqrt[4]{6}$ into a single radical.

$\sqrt[4]{\frac{36}{6}} \cdot \sqrt[4]{216}$

Combine using the product rule for radicals.

$\sqrt[4]{\frac{36}{6} \cdot 216}$

Combine $\frac{36}{6}$ and $216$ .

$\sqrt[4]{\frac{36 \cdot 216}{6}}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{36 \cdot 216}{6}$ by cancelling the common factors.

Factor $6$ out of $36 \cdot 216$ .

$\sqrt[4]{\frac{6 (6 \cdot 216)}{6}}$

Factor $6$ out of $6$ .

$\sqrt[4]{\frac{6 (6 \cdot 216)}{6 (1)}}$

Cancel the common factor.

$\sqrt[4]{\frac{6 (6 \cdot 216)}{6 \cdot 1}}$

Rewrite the expression.

$\sqrt[4]{\frac{6 \cdot 216}{1}}$

Divide $6 \cdot 216$ by $1$ .

$\sqrt[4]{6 \cdot 216}$

Multiply $6$ by $216$ .

$\sqrt[4]{1296}$

Rewrite $1296$ as $6^{4}$ .

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

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

$6$