Simplify cube root of 81x^3

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

Step 1

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

Factor $27$ out of $81$ .

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

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

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

Move $3$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

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

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