Trigonometry Examples

$2 \sqrt[3]{16 x^{3} y^{4} z^{5}}$

Step 1

Rewrite $16 x^{3} y^{4} z^{5}$ as ${(2 x y z)}^{3} \cdot (2 y z^{2})$ .

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Step 1.1

Factor $8$ out of $16$ .

$2 \sqrt[3]{8 (2) x^{3} y^{4} z^{5}}$

Step 1.2

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

$2 \sqrt[3]{2^{3} \cdot 2 x^{3} y^{4} z^{5}}$

Step 1.3

Factor out $y^{3}$ .

$2 \sqrt[3]{2^{3} \cdot 2 x^{3} (y^{3} y) z^{5}}$

Step 1.4

Factor out $z^{3}$ .

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

Step 1.5

Move $y$ .

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

Step 1.6

Move $2$ .

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

Step 1.7

Rewrite $(2^{3} x^{3} (y^{3})) z^{3}$ as ${(2 x y z)}^{3}$ .

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

Step 1.8

Add parentheses.

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

Step 1.9

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $2$ by $2$ .

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