Algebra Examples

$(2 \sqrt[4]{8 y^{2}}) (- 2 \sqrt[4]{12 y^{3}})$

Step 1

Multiply $(2 \sqrt[4]{8 y^{2}}) (- 2 \sqrt[4]{12 y^{3}})$ .

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Step 1.1

Multiply $- 2$ by $2$ .

$- 4 \sqrt[4]{8 y^{2}} \sqrt[4]{12 y^{3}}$

Step 1.2

Combine using the product rule for radicals.

$- 4 \sqrt[4]{12 y^{3} (8 y^{2})}$

Step 1.3

Multiply $8$ by $12$ .

$- 4 \sqrt[4]{96 y^{3} y^{2}}$

Step 1.4

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

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Step 1.4.1

Move $y^{2}$ .

$- 4 \sqrt[4]{96 (y^{2} y^{3})}$

Step 1.4.2

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

$- 4 \sqrt[4]{96 y^{2 + 3}}$

Step 1.4.3

Add $2$ and $3$ .

$- 4 \sqrt[4]{96 y^{5}}$

Step 2

Rewrite $96 y^{5}$ as ${(2 y)}^{4} \cdot (6 y)$ .

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Step 2.1

Factor $16$ out of $96$ .

$- 4 \sqrt[4]{16 (6) y^{5}}$

Step 2.2

Rewrite $16$ as $2^{4}$ .

$- 4 \sqrt[4]{2^{4} \cdot 6 y^{5}}$

Step 2.3

Factor out $y^{4}$ .

$- 4 \sqrt[4]{2^{4} \cdot 6 (y^{4} y)}$

Step 2.4

Move $6$ .

$- 4 \sqrt[4]{2^{4} y^{4} \cdot 6 y}$

Step 2.5

Rewrite $2^{4} y^{4}$ as ${(2 y)}^{4}$ .

$- 4 \sqrt[4]{{(2 y)}^{4} \cdot 6 y}$

Step 2.6

Add parentheses.

$- 4 \sqrt[4]{{(2 y)}^{4} \cdot (6 y)}$

Step 3

Pull terms out from under the radical.

$- 4 (2 y \sqrt[4]{6 y})$

Step 4

Multiply $2$ by $- 4$ .

$- 8 y \sqrt[4]{6 y}$