Algebra Examples

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

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

Factor $9$ out of $9$ .

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

Step 1.1.3

Cancel the common factor.

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

Step 1.1.4

Rewrite the expression.

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

Step 1.2

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Pull terms out from under the radical.

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