Simplify fourth root of 256x^4* cube root of 27x

$\sqrt[4]{256 x^{4}} \cdot \sqrt[3]{27 x}$

Rewrite $256 x^{4}$ as ${(4 x)}^{4}$ .

$\sqrt[4]{{(4 x)}^{4}} \cdot \sqrt[3]{27 x}$

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

$4 x \cdot \sqrt[3]{27 x}$

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

$4 x \cdot \sqrt[3]{3^{3} x}$

Pull terms out from under the radical.

$4 x \cdot (3 \sqrt[3]{x})$

Multiply $3$ by $4$ .

$12 x \sqrt[3]{x}$