Trigonometry Examples

$\sqrt[3]{686 a^{7} b^{9} c^{11}}$

Step 1

Rewrite $686 a^{7} b^{9} c^{11}$ as ${(7 a^{2} b^{3} c^{3})}^{3} \cdot (2 a c^{2})$ .

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Step 1.1

Factor $343$ out of $686$ .

$\sqrt[3]{343 (2) a^{7} b^{9} c^{11}}$

Step 1.2

Rewrite $343$ as $7^{3}$ .

$\sqrt[3]{7^{3} \cdot 2 a^{7} b^{9} c^{11}}$

Step 1.3

Factor out $a^{6}$ .

$\sqrt[3]{7^{3} \cdot 2 (a^{6} a) b^{9} c^{11}}$

Step 1.4

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

$\sqrt[3]{7^{3} \cdot 2 ({(a^{2})}^{3} a) b^{9} c^{11}}$

Step 1.5

Rewrite $b^{9}$ as ${(b^{3})}^{3}$ .

$\sqrt[3]{7^{3} \cdot 2 ({(a^{2})}^{3} a) {(b^{3})}^{3} c^{11}}$

Step 1.6

Factor out $c^{9}$ .

$\sqrt[3]{7^{3} \cdot 2 ({(a^{2})}^{3} a) {(b^{3})}^{3} (c^{9} c^{2})}$

Step 1.7

Rewrite $c^{9}$ as ${(c^{3})}^{3}$ .

$\sqrt[3]{7^{3} \cdot 2 ({(a^{2})}^{3} a) {(b^{3})}^{3} ({(c^{3})}^{3} c^{2})}$

Step 1.8

Move $a$ .

$\sqrt[3]{7^{3} \cdot 2 ({(a^{2})}^{3}) {(b^{3})}^{3} {(c^{3})}^{3} a c^{2}}$

Step 1.9

Move $2$ .

$\sqrt[3]{(7^{3} ({(a^{2})}^{3})) {(b^{3})}^{3} {(c^{3})}^{3} \cdot 2 a c^{2}}$

Step 1.10

Rewrite $(7^{3} ({(a^{2})}^{3})) {(b^{3})}^{3} {(c^{3})}^{3}$ as ${(7 a^{2} b^{3} c^{3})}^{3}$ .

$\sqrt[3]{{(7 a^{2} b^{3} c^{3})}^{3} \cdot 2 a c^{2}}$

Step 1.11

Add parentheses.

$\sqrt[3]{{(7 a^{2} b^{3} c^{3})}^{3} \cdot 2 (a c^{2})}$

Step 1.12

Add parentheses.

$\sqrt[3]{{(7 a^{2} b^{3} c^{3})}^{3} \cdot (2 a c^{2})}$

Step 2

Pull terms out from under the radical.

$7 a^{2} b^{3} c^{3} \sqrt[3]{2 a c^{2}}$