Pre-Algebra Examples

$\sqrt[3]{56 x^{4} y^{8}}$

Step 1

Rewrite $56 x^{4} y^{8}$ as ${(2 x y^{2})}^{3} \cdot (7 x y^{2})$ .

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Step 1.1

Factor $8$ out of $56$ .

$\sqrt[3]{8 (7) x^{4} y^{8}}$

Step 1.2

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

$\sqrt[3]{2^{3} \cdot 7 x^{4} y^{8}}$

Step 1.3

Factor out $x^{3}$ .

$\sqrt[3]{2^{3} \cdot 7 (x^{3} x) y^{8}}$

Step 1.4

Factor out $y^{6}$ .

$\sqrt[3]{2^{3} \cdot 7 (x^{3} x) (y^{6} y^{2})}$

Step 1.5

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

$\sqrt[3]{2^{3} \cdot 7 (x^{3} x) ({(y^{2})}^{3} y^{2})}$

Step 1.6

Move $x$ .

$\sqrt[3]{2^{3} \cdot 7 (x^{3}) {(y^{2})}^{3} x y^{2}}$

Step 1.7

Move $7$ .

$\sqrt[3]{2^{3} (x^{3}) {(y^{2})}^{3} \cdot 7 x y^{2}}$

Step 1.8

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

$\sqrt[3]{{(2 x y^{2})}^{3} \cdot 7 x y^{2}}$

Step 1.9

Add parentheses.

$\sqrt[3]{{(2 x y^{2})}^{3} \cdot 7 (x y^{2})}$

Step 1.10

Add parentheses.

$\sqrt[3]{{(2 x y^{2})}^{3} \cdot (7 x y^{2})}$

Step 2

Pull terms out from under the radical.

$2 x y^{2} \sqrt[3]{7 x y^{2}}$