Simplify fourth root of (2x)^8

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

Step 1

Simplify the expression.

Apply the product rule to $2 x$ .

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

Raise $2$ to the power of $8$ .

$\sqrt[4]{256 x^{8}}$

Step 2

Rewrite $256 x^{8}$ as ${(4 x^{2})}^{4}$ .

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

Step 3

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

$4 x^{2}$