Simplify fourth root of 8x^2* fourth root of 2x^2

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

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

Combine using the product rule for radicals.

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

Multiply $2$ by $8$ .

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

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

$\sqrt[4]{16 x^{4}}$

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

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

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

$2 x$