Algebra Examples

$2 \sqrt[3]{192 p^{7} q^{18}}$

Step 1

Rewrite $192 p^{7} q^{18}$ as ${(4 p^{2} q^{6})}^{3} \cdot (3 p)$ .

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Step 1.1

Factor $64$ out of $192$ .

$2 \sqrt[3]{64 (3) p^{7} q^{18}}$

Step 1.2

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

$2 \sqrt[3]{4^{3} \cdot 3 p^{7} q^{18}}$

Step 1.3

Factor out $p^{6}$ .

$2 \sqrt[3]{4^{3} \cdot 3 (p^{6} p) q^{18}}$

Step 1.4

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

$2 \sqrt[3]{4^{3} \cdot 3 ({(p^{2})}^{3} p) q^{18}}$

Step 1.5

Rewrite $q^{18}$ as ${(q^{6})}^{3}$ .

$2 \sqrt[3]{4^{3} \cdot 3 ({(p^{2})}^{3} p) {(q^{6})}^{3}}$

Step 1.6

Move $p$ .

$2 \sqrt[3]{4^{3} \cdot 3 ({(p^{2})}^{3}) {(q^{6})}^{3} p}$

Step 1.7

Move $3$ .

$2 \sqrt[3]{4^{3} ({(p^{2})}^{3}) {(q^{6})}^{3} \cdot 3 p}$

Step 1.8

Rewrite $(4^{3} ({(p^{2})}^{3})) {(q^{6})}^{3}$ as ${(4 p^{2} q^{6})}^{3}$ .

$2 \sqrt[3]{{(4 p^{2} q^{6})}^{3} \cdot 3 p}$

Step 1.9

Add parentheses.

$2 \sqrt[3]{{(4 p^{2} q^{6})}^{3} \cdot (3 p)}$

Step 2

Pull terms out from under the radical.

$2 (4 p^{2} q^{6} \sqrt[3]{3 p})$

Step 3

Multiply $4$ by $2$ .

$8 p^{2} q^{6} \sqrt[3]{3 p}$