Pre-Algebra Examples

$\sqrt[3]{- 81 x^{10} y^{8}}$

Step 1

Rewrite $- 81 x^{10} y^{8}$ as ${(- 3 x^{3} y^{2})}^{3} \cdot (3 x y^{2})$ .

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Step 1.1

Factor $- 27$ out of $- 81$ .

$\sqrt[3]{- 27 (3) x^{10} y^{8}}$

Step 1.2

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

$\sqrt[3]{{(- 3)}^{3} \cdot 3 x^{10} y^{8}}$

Step 1.3

Factor out $x^{9}$ .

$\sqrt[3]{{(- 3)}^{3} \cdot 3 (x^{9} x) y^{8}}$

Step 1.4

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

$\sqrt[3]{{(- 3)}^{3} \cdot 3 ({(x^{3})}^{3} x) y^{8}}$

Step 1.5

Factor out $y^{6}$ .

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

Step 1.6

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

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

Step 1.7

Move $x$ .

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

Step 1.8

Move $3$ .

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

Step 1.9

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

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

Step 1.10

Add parentheses.

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

Step 1.11

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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