Simplify 2( fourth root of 16x)-2 fourth root of 2y+3( fourth root of 81x)-4 fourth root of 32y

$2 (\sqrt[4]{16 x}) - 2 \sqrt[4]{2 y} + 3 (\sqrt[4]{81 x}) - 4 \sqrt[4]{32 y}$

Step 1

Simplify each term.

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

$2 \sqrt[4]{2^{4} x} - 2 \sqrt[4]{2 y} + 3 (\sqrt[4]{81 x}) - 4 \sqrt[4]{32 y}$

Pull terms out from under the radical.

$2 (2 \sqrt[4]{x}) - 2 \sqrt[4]{2 y} + 3 (\sqrt[4]{81 x}) - 4 \sqrt[4]{32 y}$

Multiply $2$ by $2$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 3 (\sqrt[4]{81 x}) - 4 \sqrt[4]{32 y}$

Rewrite $81$ as $3^{4}$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 3 \sqrt[4]{3^{4} x} - 4 \sqrt[4]{32 y}$

Pull terms out from under the radical.

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 3 (3 \sqrt[4]{x}) - 4 \sqrt[4]{32 y}$

Multiply $3$ by $3$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 4 \sqrt[4]{32 y}$

Rewrite $32 y$ as $2^{4} \cdot (2 y)$ .

Factor $16$ out of $32$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 4 \sqrt[4]{16 (2) y}$

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

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 4 \sqrt[4]{2^{4} \cdot 2 y}$

Add parentheses.

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 4 \sqrt[4]{2^{4} \cdot (2 y)}$

Pull terms out from under the radical.

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 4 (2 \sqrt[4]{2 y})$

Multiply $2$ by $- 4$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 8 \sqrt[4]{2 y}$

Step 2

Simplify by adding terms.

Add $4 \sqrt[4]{x}$ and $9 \sqrt[4]{x}$ .

$13 \sqrt[4]{x} - 2 \sqrt[4]{2 y} - 8 \sqrt[4]{2 y}$

Subtract $8 \sqrt[4]{2 y}$ from $- 2 \sqrt[4]{2 y}$ .

$13 \sqrt[4]{x} - 10 \sqrt[4]{2 y}$