Finite Math Examples

$4 \sqrt[3]{864 x^{5} y^{14}}$

Step 1

Rewrite $864 x^{5} y^{14}$ as ${(6 x y^{4})}^{3} \cdot (4 x^{2} y^{2})$ .

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Step 1.1

Factor $216$ out of $864$ .

$4 \sqrt[3]{216 (4) x^{5} y^{14}}$

Step 1.2

Rewrite $216$ as $6^{3}$ .

$4 \sqrt[3]{6^{3} \cdot 4 x^{5} y^{14}}$

Step 1.3

Factor out $x^{3}$ .

$4 \sqrt[3]{6^{3} \cdot 4 (x^{3} x^{2}) y^{14}}$

Step 1.4

Factor out $y^{12}$ .

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

Step 1.5

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

$4 \sqrt[3]{6^{3} \cdot 4 (x^{3} x^{2}) ({(y^{4})}^{3} y^{2})}$

Step 1.6

Move $x^{2}$ .

$4 \sqrt[3]{6^{3} \cdot 4 (x^{3}) {(y^{4})}^{3} x^{2} y^{2}}$

Step 1.7

Move $4$ .

$4 \sqrt[3]{6^{3} (x^{3}) {(y^{4})}^{3} \cdot 4 x^{2} y^{2}}$

Step 1.8

Rewrite $(6^{3} (x^{3})) {(y^{4})}^{3}$ as ${(6 x y^{4})}^{3}$ .

$4 \sqrt[3]{{(6 x y^{4})}^{3} \cdot 4 x^{2} y^{2}}$

Step 1.9

Add parentheses.

$4 \sqrt[3]{{(6 x y^{4})}^{3} \cdot 4 (x^{2} y^{2})}$

Step 1.10

Add parentheses.

$4 \sqrt[3]{{(6 x y^{4})}^{3} \cdot (4 x^{2} y^{2})}$

Step 2

Pull terms out from under the radical.

$4 (6 x y^{4} \sqrt[3]{4 x^{2} y^{2}})$

Step 3

Multiply $6$ by $4$ .

$24 x y^{4} \sqrt[3]{4 x^{2} y^{2}}$