Simplify ( cube root of 54)/( sixth root of 4)

$\frac{\sqrt[3]{54}}{\sqrt[6]{4}}$

Simplify the numerator.

Rewrite $54$ as $3^{3} \cdot 2$ .

Factor $27$ out of $54$ .

$\frac{\sqrt[3]{27 (2)}}{\sqrt[6]{4}}$

Rewrite $27$ as $3^{3}$ .

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

Pull terms out from under the radical.

$\frac{3 \sqrt[3]{2}}{\sqrt[6]{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

Rewrite $\sqrt[6]{2^{2}}$ as $\sqrt[3]{\sqrt{2^{2}}}$ .

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

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

$\frac{3 \sqrt[3]{2}}{\sqrt[3]{2}}$

Cancel the common factor of $\sqrt[3]{2}$ .

Cancel the common factor.

$\frac{3 \sqrt[3]{2}}{\sqrt[3]{2}}$

Divide $3$ by $1$ .

$3$