Algebra Examples

$x \sqrt[3]{56 x^{4} y^{5}}$

Step 1

Rewrite $56 x^{4} y^{5}$ as ${(2 x y)}^{3} \cdot (7 x y^{2})$ .

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Step 1.1

Factor $8$ out of $56$ .

$x \sqrt[3]{8 (7) x^{4} y^{5}}$

Step 1.2

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

$x \sqrt[3]{2^{3} \cdot 7 x^{4} y^{5}}$

Step 1.3

Factor out $x^{3}$ .

$x \sqrt[3]{2^{3} \cdot 7 (x^{3} x) y^{5}}$

Step 1.4

Factor out $y^{3}$ .

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

Step 1.5

Move $x$ .

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

Step 1.6

Move $7$ .

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

Step 1.7

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

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

Step 1.8

Add parentheses.

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

Step 1.9

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $x$ by $x$ by adding the exponents.

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Step 4.1

Move $x$ .

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

Step 4.2

Multiply $x$ by $x$ .

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

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