Simplify cube root of -500/(x^12)

$\sqrt[3]{\frac{- 500}{x^{12}}}$

Step 1

Move the negative in front of the fraction.

$\sqrt[3]{- \frac{500}{x^{12}}}$

Step 2

Rewrite $- \frac{500}{x^{12}}$ as ${(- \frac{5}{x^{4}})}^{3} \cdot 4$ .

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

$\sqrt[3]{{(- 1)}^{3} \frac{500}{x^{12}}}$

Factor the perfect power $5^{3}$ out of $500$ .

$\sqrt[3]{{(- 1)}^{3} \frac{5^{3} \cdot 4}{x^{12}}}$

Factor the perfect power ${(x^{4})}^{3}$ out of $x^{12}$ .

$\sqrt[3]{{(- 1)}^{3} \frac{5^{3} \cdot 4}{{(x^{4})}^{3} \cdot 1}}$

Rearrange the fraction $\frac{5^{3} \cdot 4}{{(x^{4})}^{3} \cdot 1}$ .

$\sqrt[3]{{(- 1)}^{3} ({(\frac{5}{x^{4}})}^{3} \cdot 4)}$

Rewrite ${(- 1)}^{3} {(\frac{5}{x^{4}})}^{3}$ as ${(- \frac{5}{x^{4}})}^{3}$ .

$\sqrt[3]{{(- \frac{5}{x^{4}})}^{3} \cdot 4}$

Step 3

Pull terms out from under the radical.

$- \frac{5}{x^{4}} \sqrt[3]{4}$

Step 4

Combine $\sqrt[3]{4}$ and $\frac{5}{x^{4}}$ .

$- \frac{\sqrt[3]{4} \cdot 5}{x^{4}}$

Step 5

Move $5$ to the left of $\sqrt[3]{4}$ .

$- \frac{5 \sqrt[3]{4}}{x^{4}}$