Basic Math Examples

$\sqrt[3]{32 a^{2} b^{7}} - \sqrt[3]{4 a^{8} b}$

Step 1

Rewrite $32 a^{2} b^{7}$ as ${(2 b^{2})}^{3} \cdot (4 a^{2} b)$ .

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Step 1.1

Factor $8$ out of $32$ .

$\sqrt[3]{8 (4) a^{2} b^{7}} - \sqrt[3]{4 a^{8} b}$

Step 1.2

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} \cdot 4 a^{2} b^{7}} - \sqrt[3]{4 a^{8} b}$

Step 1.3

Factor out $b^{6}$ .

$\sqrt[3]{2^{3} \cdot 4 a^{2} (b^{6} b)} - \sqrt[3]{4 a^{8} b}$

Step 1.4

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

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

Step 1.5

Move $a^{2}$ .

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

Step 1.6

Move $4$ .

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

Step 1.7

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

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

Step 1.8

Add parentheses.

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

Step 1.9

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite $4 a^{8} b$ as ${(a^{2})}^{3} \cdot (4 a^{2} b)$ .

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Step 3.1

Factor out $a^{6}$ .

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

Step 3.2

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

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

Step 3.3

Reorder $4$ and ${(a^{2})}^{3}$ .

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

Step 3.4

Add parentheses.

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

Step 3.5

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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