Algebra Examples

$\sqrt[3]{128 a^{13} b^{6}}$

Step 1

Rewrite $128 a^{13} b^{6}$ as ${(4 a^{4} b^{2})}^{3} \cdot (2 a)$ .

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Step 1.1

Factor $64$ out of $128$ .

$\sqrt[3]{64 (2) a^{13} b^{6}}$

Step 1.2

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{4^{3} \cdot 2 a^{13} b^{6}}$

Step 1.3

Factor out $a^{12}$ .

$\sqrt[3]{4^{3} \cdot 2 (a^{12} a) b^{6}}$

Step 1.4

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

$\sqrt[3]{4^{3} \cdot 2 ({(a^{4})}^{3} a) b^{6}}$

Step 1.5

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

$\sqrt[3]{4^{3} \cdot 2 ({(a^{4})}^{3} a) {(b^{2})}^{3}}$

Step 1.6

Move $a$ .

$\sqrt[3]{4^{3} \cdot 2 ({(a^{4})}^{3}) {(b^{2})}^{3} a}$

Step 1.7

Move $2$ .

$\sqrt[3]{4^{3} ({(a^{4})}^{3}) {(b^{2})}^{3} \cdot 2 a}$

Step 1.8

Rewrite $(4^{3} ({(a^{4})}^{3})) {(b^{2})}^{3}$ as ${(4 a^{4} b^{2})}^{3}$ .

$\sqrt[3]{{(4 a^{4} b^{2})}^{3} \cdot 2 a}$

Step 1.9

Add parentheses.

$\sqrt[3]{{(4 a^{4} b^{2})}^{3} \cdot (2 a)}$

Step 2

Pull terms out from under the radical.

$4 a^{4} b^{2} \sqrt[3]{2 a}$