Simplify fourth root of 16x^2* square root of 100x^12

$\sqrt[4]{16 x^{2}} \cdot \sqrt{100 x^{12}}$

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

$\sqrt[4]{2^{4} x^{2}} \cdot \sqrt{100 x^{12}}$

Pull terms out from under the radical.

$2 \sqrt[4]{x^{2}} \cdot \sqrt{100 x^{12}}$

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

$2 \sqrt{\sqrt{x^{2}}} \cdot \sqrt{100 x^{12}}$

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

$2 \sqrt{x} \cdot \sqrt{100 x^{12}}$

Rewrite $100 x^{12}$ as ${(10 x^{6})}^{2}$ .

$2 \sqrt{x} \cdot \sqrt{{(10 x^{6})}^{2}}$

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

$2 \sqrt{x} \cdot (10 x^{6})$

Multiply $10$ by $2$ .

$20 \sqrt{x} x^{6}$