Simplify ( cube root of -80x^9)/( cube root of 2x^2)

$\frac{\sqrt[3]{- 80 x^{9}}}{\sqrt[3]{2 x^{2}}}$

Combine $\sqrt[3]{- 80 x^{9}}$ and $\sqrt[3]{2 x^{2}}$ into a single radical.

$\sqrt[3]{\frac{- 80 x^{9}}{2 x^{2}}}$

Reduce the expression $\frac{- 80 x^{9}}{2 x^{2}}$ by cancelling the common factors.

Factor $2$ out of $- 80 x^{9}$ .

$\sqrt[3]{\frac{2 (- 40 x^{9})}{2 x^{2}}}$

Factor $2$ out of $2 x^{2}$ .

$\sqrt[3]{\frac{2 (- 40 x^{9})}{2 (x^{2})}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 (- 40 x^{9})}{2 x^{2}}}$

Rewrite the expression.

$\sqrt[3]{\frac{- 40 x^{9}}{x^{2}}}$

Cancel the common factor of $x^{9}$ and $x^{2}$ .

Factor $x^{2}$ out of $- 40 x^{9}$ .

$\sqrt[3]{\frac{x^{2} (- 40 x^{7})}{x^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{x^{2} (- 40 x^{7})}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} (- 40 x^{7})}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{- 40 x^{7}}{1}}$

Divide $- 40 x^{7}$ by $1$ .

$\sqrt[3]{- 40 x^{7}}$

Rewrite $- 40 x^{7}$ as ${(- 2 x^{2})}^{3} \cdot (5 x)$ .

Factor $- 8$ out of $- 40$ .

$\sqrt[3]{- 8 (5) x^{7}}$

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

$\sqrt[3]{{(- 2)}^{3} \cdot 5 x^{7}}$

Factor out $x^{6}$ .

$\sqrt[3]{{(- 2)}^{3} \cdot 5 (x^{6} x)}$

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

$\sqrt[3]{{(- 2)}^{3} \cdot 5 ({(x^{2})}^{3} x)}$

Move $5$ .

$\sqrt[3]{{(- 2)}^{3} {(x^{2})}^{3} \cdot 5 x}$

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

$\sqrt[3]{{(- 2 x^{2})}^{3} \cdot 5 x}$

Add parentheses.

$\sqrt[3]{{(- 2 x^{2})}^{3} \cdot (5 x)}$

Pull terms out from under the radical.

$- 2 x^{2} \sqrt[3]{5 x}$