Simplify (2 fourth root of 8y^2)(-2 fourth root of 12y^3)

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

Step 1

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

Multiply $- 2$ by $2$ .

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

Combine using the product rule for radicals.

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

Multiply $8$ by $12$ .

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

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

Move $y^{2}$ .

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

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

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

Add $2$ and $3$ .

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

Step 2

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

Factor $16$ out of $96$ .

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

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

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

Factor out $y^{4}$ .

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

Move $6$ .

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

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

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

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 $- 4$ .

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