Simplify - cube root of -54d^9ef

$- \sqrt[3]{- 54 d^{9} e f}$

Rewrite $- 54 d^{9} e f$ as ${(- 3 d^{3})}^{3} \cdot (2 e f)$ .

Factor $- 27$ out of $- 54$ .

$- \sqrt[3]{- 27 (2) d^{9} e f}$

Rewrite $- 27$ as ${(- 3)}^{3}$ .

$- \sqrt[3]{{(- 3)}^{3} \cdot 2 d^{9} e f}$

Rewrite $d^{9}$ as ${(d^{3})}^{3}$ .

$- \sqrt[3]{{(- 3)}^{3} \cdot 2 {(d^{3})}^{3} e f}$

Move $2$ .

$- \sqrt[3]{{(- 3)}^{3} {(d^{3})}^{3} \cdot 2 e f}$

Rewrite ${(- 3)}^{3} {(d^{3})}^{3}$ as ${(- 3 d^{3})}^{3}$ .

$- \sqrt[3]{{(- 3 d^{3})}^{3} \cdot 2 e f}$

Add parentheses.

$- \sqrt[3]{{(- 3 d^{3})}^{3} \cdot 2 (e f)}$

Add parentheses.

$- \sqrt[3]{{(- 3 d^{3})}^{3} \cdot (2 e f)}$

Pull terms out from under the radical.

$- (- 3 d^{3} \sqrt[3]{2 e f})$

Multiply $- 3$ by $- 1$ .

$3 d^{3} \sqrt[3]{2 e f}$