Simplify cube root of (27a^12)/9

$\sqrt[3]{\frac{27 a^{12}}{9}}$

Step 1

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{27 a^{12}}{9}$ by cancelling the common factors.

Factor $9$ out of $27 a^{12}$ .

$\sqrt[3]{\frac{9 (3 a^{12})}{9}}$

Factor $9$ out of $9$ .

$\sqrt[3]{\frac{9 (3 a^{12})}{9 (1)}}$

Cancel the common factor.

$\sqrt[3]{\frac{9 (3 a^{12})}{9 \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{3 a^{12}}{1}}$

Divide $3 a^{12}$ by $1$ .

$\sqrt[3]{3 a^{12}}$

Step 2

Rewrite $3 a^{12}$ as ${(a^{4})}^{3} \cdot 3$ .

Rewrite $a^{12}$ as ${(a^{4})}^{3}$ .

$\sqrt[3]{3 {(a^{4})}^{3}}$

Reorder $3$ and ${(a^{4})}^{3}$ .

$\sqrt[3]{{(a^{4})}^{3} \cdot 3}$

Step 3

Pull terms out from under the radical.

$a^{4} \sqrt[3]{3}$