Simplify cube root of 81x^7

$\sqrt[3]{81 x^{7}}$

Step 1

Rewrite $81 x^{7}$ as ${(3 x^{2})}^{3} \cdot (3 x)$ .

Factor $27$ out of $81$ .

$\sqrt[3]{27 (3) x^{7}}$

Rewrite $27$ as $3^{3}$ .

$\sqrt[3]{3^{3} \cdot 3 x^{7}}$

Factor out $x^{6}$ .

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

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

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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