Simplify -8 fourth root of 324x^2

$- 8 \sqrt[4]{324 x^{2}}$

Step 1

Rewrite $324 x^{2}$ as $3^{4} \cdot (4 x^{2})$ .

Factor $81$ out of $324$ .

$- 8 \sqrt[4]{81 (4) x^{2}}$

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

$- 8 \sqrt[4]{3^{4} \cdot 4 x^{2}}$

Add parentheses.

$- 8 \sqrt[4]{3^{4} \cdot (4 x^{2})}$

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

Step 4

Rewrite $\sqrt[4]{{(2 x)}^{2}}$ as $\sqrt{\sqrt{{(2 x)}^{2}}}$ .

$- 8 (3 \sqrt{\sqrt{{(2 x)}^{2}}})$

Step 5

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

$- 8 (3 \sqrt{2 x})$

Step 6

Multiply $3$ by $- 8$ .

$- 24 \sqrt{2 x}$