Simplify 4 sixth root of -64x^3

$4 \sqrt[6]{- 64 x^{3}}$

Rewrite $- 64 x^{3}$ as $2^{6} \cdot (- 1 x^{3})$ .

Factor $64$ out of $- 64$ .

$4 \sqrt[6]{64 (- 1) x^{3}}$

Rewrite $64$ as $2^{6}$ .

$4 \sqrt[6]{2^{6} \cdot - 1 x^{3}}$

Add parentheses.

$4 \sqrt[6]{2^{6} \cdot (- 1 x^{3})}$

Pull terms out from under the radical.

$4 (2 \sqrt[6]{- 1 x^{3}})$

Rewrite $- 1 x^{3}$ as ${(- x)}^{3}$ .

$4 (2 \sqrt[6]{{(- x)}^{3}})$

Rewrite $\sqrt[6]{{(- x)}^{3}}$ as $\sqrt{\sqrt[3]{{(- x)}^{3}}}$ .

$4 (2 \sqrt{\sqrt[3]{{(- x)}^{3}}})$

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

$4 (2 \sqrt{- x})$

Multiply $2$ by $4$ .

$8 \sqrt{- x}$