Finite Math Examples

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

Step 1

Multiply $3 \sqrt[4]{3 y} \sqrt[4]{y^{3}}$ .

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Step 1.1

Combine using the product rule for radicals.

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

Step 1.2

Multiply $y^{3}$ by $y$ by adding the exponents.

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Step 1.2.1

Move $y$ .

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

Step 1.2.2

Multiply $y$ by $y^{3}$ .

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Step 1.2.2.1

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

$2 x y \sqrt[4]{y} \cdot (3 \sqrt[4]{y^{1} y^{3} \cdot 3})$

Step 1.2.2.2

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

$2 x y \sqrt[4]{y} \cdot (3 \sqrt[4]{y^{1 + 3} \cdot 3})$

Step 1.2.3

Add $1$ and $3$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1

Move $y$ .

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

Step 3.2

Multiply $y$ by $y$ .

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

Step 4

Multiply $2 x y^{2} \sqrt[4]{y} (3 \sqrt[4]{3})$ .

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Step 4.1

Multiply $3$ by $2$ .

$6 x y^{2} \sqrt[4]{y} \sqrt[4]{3}$

Step 4.2

Combine using the product rule for radicals.

$6 x y^{2} \sqrt[4]{3 y}$