Simplify 6 fourth root of 32x- fourth root of 512x+ fourth root of 16x^4

$6 \sqrt[4]{32 x} - \sqrt[4]{512 x} + \sqrt[4]{16 x^{4}}$

Step 1

Simplify each term.

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

Factor $16$ out of $32$ .

$6 \sqrt[4]{16 (2) x} - \sqrt[4]{512 x} + \sqrt[4]{16 x^{4}}$

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

$6 \sqrt[4]{2^{4} \cdot 2 x} - \sqrt[4]{512 x} + \sqrt[4]{16 x^{4}}$

Add parentheses.

$6 \sqrt[4]{2^{4} \cdot (2 x)} - \sqrt[4]{512 x} + \sqrt[4]{16 x^{4}}$

Pull terms out from under the radical.

$6 (2 \sqrt[4]{2 x}) - \sqrt[4]{512 x} + \sqrt[4]{16 x^{4}}$

Multiply $2$ by $6$ .

$12 \sqrt[4]{2 x} - \sqrt[4]{512 x} + \sqrt[4]{16 x^{4}}$

Rewrite $512 x$ as $4^{4} \cdot (2 x)$ .

Factor $256$ out of $512$ .

$12 \sqrt[4]{2 x} - \sqrt[4]{256 (2) x} + \sqrt[4]{16 x^{4}}$

Rewrite $256$ as $4^{4}$ .

$12 \sqrt[4]{2 x} - \sqrt[4]{4^{4} \cdot 2 x} + \sqrt[4]{16 x^{4}}$

Add parentheses.

$12 \sqrt[4]{2 x} - \sqrt[4]{4^{4} \cdot (2 x)} + \sqrt[4]{16 x^{4}}$

Pull terms out from under the radical.

$12 \sqrt[4]{2 x} - (4 \sqrt[4]{2 x}) + \sqrt[4]{16 x^{4}}$

Multiply $4$ by $- 1$ .

$12 \sqrt[4]{2 x} - 4 \sqrt[4]{2 x} + \sqrt[4]{16 x^{4}}$

Rewrite $16 x^{4}$ as ${(2 x)}^{4}$ .

$12 \sqrt[4]{2 x} - 4 \sqrt[4]{2 x} + \sqrt[4]{{(2 x)}^{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$12 \sqrt[4]{2 x} - 4 \sqrt[4]{2 x} + 2 x$

Step 2

Subtract $4 \sqrt[4]{2 x}$ from $12 \sqrt[4]{2 x}$ .

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