Simplify cube root of -8d^2f^5

$\sqrt[3]{- 8 d^{2} f^{5}}$

Step 1

Rewrite $- 8 d^{2} f^{5}$ as ${(- 2 f)}^{3} (d^{2} f^{2})$ .

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$\sqrt[3]{{(- 2)}^{3} d^{2} f^{5}}$

Factor out $f^{3}$ .

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

Move $d^{2}$ .

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

Rewrite ${(- 2)}^{3} f^{3}$ as ${(- 2 f)}^{3}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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