Simplify - cube root of (81y^2)/(1000x^3)

$- \sqrt[3]{\frac{81 y^{2}}{1000 x^{3}}}$

Step 1

Rewrite $\frac{81 y^{2}}{1000 x^{3}}$ as ${(\frac{3}{10 x})}^{3} (3 y^{2})$ .

Factor the perfect power $3^{3}$ out of $81 y^{2}$ .

$- \sqrt[3]{\frac{3^{3} \cdot (3 y^{2})}{1000 x^{3}}}$

Factor the perfect power ${(10 x)}^{3}$ out of $1000 x^{3}$ .

$- \sqrt[3]{\frac{3^{3} \cdot (3 y^{2})}{{(10 x)}^{3} \cdot 1}}$

Rearrange the fraction $\frac{3^{3} \cdot (3 y^{2})}{{(10 x)}^{3} \cdot 1}$ .

$- \sqrt[3]{{(\frac{3}{10 x})}^{3} (3 y^{2})}$

Step 2

Pull terms out from under the radical.

$- (\frac{3}{10 x} \sqrt[3]{3 y^{2}})$

Step 3

Combine $\frac{3}{10 x}$ and $\sqrt[3]{3 y^{2}}$ .

$- \frac{3 \sqrt[3]{3 y^{2}}}{10 x}$