Finite Math Examples

$\sqrt[3]{128 a^{2} b^{13}} - \sqrt[3]{2 a^{8} b}$

Step 1

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

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Step 1.1

Factor $64$ out of $128$ .

$\sqrt[3]{64 (2) a^{2} b^{13}} - \sqrt[3]{2 a^{8} b}$

Step 1.2

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

$\sqrt[3]{4^{3} \cdot 2 a^{2} b^{13}} - \sqrt[3]{2 a^{8} b}$

Step 1.3

Factor out $b^{12}$ .

$\sqrt[3]{4^{3} \cdot 2 a^{2} (b^{12} b)} - \sqrt[3]{2 a^{8} b}$

Step 1.4

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

$\sqrt[3]{4^{3} \cdot 2 a^{2} ({(b^{4})}^{3} b)} - \sqrt[3]{2 a^{8} b}$

Step 1.5

Move $a^{2}$ .

$\sqrt[3]{4^{3} \cdot 2 {(b^{4})}^{3} a^{2} b} - \sqrt[3]{2 a^{8} b}$

Step 1.6

Move $2$ .

$\sqrt[3]{4^{3} {(b^{4})}^{3} \cdot 2 a^{2} b} - \sqrt[3]{2 a^{8} b}$

Step 1.7

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

$\sqrt[3]{{(4 b^{4})}^{3} \cdot 2 a^{2} b} - \sqrt[3]{2 a^{8} b}$

Step 1.8

Add parentheses.

$\sqrt[3]{{(4 b^{4})}^{3} \cdot 2 (a^{2} b)} - \sqrt[3]{2 a^{8} b}$

Step 1.9

Add parentheses.

$\sqrt[3]{{(4 b^{4})}^{3} \cdot (2 a^{2} b)} - \sqrt[3]{2 a^{8} b}$

Step 2

Pull terms out from under the radical.

$4 b^{4} \sqrt[3]{2 a^{2} b} - \sqrt[3]{2 a^{8} b}$

Step 3

Rewrite $2 a^{8} b$ as ${(a^{2})}^{3} \cdot (2 a^{2} b)$ .

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Step 3.1

Factor out $a^{6}$ .

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

Step 3.2

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

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

Step 3.3

Reorder $2$ and ${(a^{2})}^{3}$ .

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

Step 3.4

Add parentheses.

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

Step 3.5

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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