Trigonometry Examples

$\sqrt[3]{- 108 x^{13} y^{14}}$

Step 1

Rewrite $- 108 x^{13} y^{14}$ as ${(- 3 x^{4} y^{4})}^{3} \cdot (4 x y^{2})$ .

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Step 1.1

Factor $- 27$ out of $- 108$ .

$\sqrt[3]{- 27 (4) x^{13} y^{14}}$

Step 1.2

Rewrite $- 27$ as ${(- 3)}^{3}$ .

$\sqrt[3]{{(- 3)}^{3} \cdot 4 x^{13} y^{14}}$

Step 1.3

Factor out $x^{12}$ .

$\sqrt[3]{{(- 3)}^{3} \cdot 4 (x^{12} x) y^{14}}$

Step 1.4

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

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

Step 1.5

Factor out $y^{12}$ .

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

Step 1.6

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

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

Step 1.7

Move $x$ .

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

Step 1.8

Move $4$ .

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

Step 1.9

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

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

Step 1.10

Add parentheses.

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

Step 1.11

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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