Simplify fifth root of -243x^9y

$\sqrt[5]{- 243 x^{9} y}$

Step 1

Rewrite $- 243 x^{9} y$ as ${(- 3 x)}^{5} (x^{4} y)$ .

Rewrite $- 243$ as ${(- 3)}^{5}$ .

$\sqrt[5]{{(- 3)}^{5} x^{9} y}$

Factor out $x^{5}$ .

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

Rewrite ${(- 3)}^{5} x^{5}$ as ${(- 3 x)}^{5}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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