Algebra Examples

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

Step 1

Rewrite $8 x^{8} y^{3}$ as ${(2 x^{2} y)}^{3} x^{2}$ .

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Step 1.1

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

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

Step 1.2

Factor out $x^{6}$ .

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

Step 1.3

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

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

Step 1.4

Move $x^{2}$ .

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

Step 1.5

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 4.1

Move $y$ .

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

Step 4.2

Multiply $y$ by $y^{2}$ .

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Step 4.2.1

Raise $y$ to the power of $1$ .

$2 (y^{1} y^{2}) (x^{2} \sqrt[3]{x^{2}})$

Step 4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 y^{1 + 2} (x^{2} \sqrt[3]{x^{2}})$

Step 4.3

Add $1$ and $2$ .

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

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