Simplify fourth root of (x^10)/16

$\sqrt[4]{\frac{x^{10}}{16}}$

Rewrite $\frac{x^{10}}{16}$ as ${(\frac{x^{2}}{2})}^{4} x^{2}$ .

Factor the perfect power ${(x^{2})}^{4}$ out of $x^{10}$ .

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

Factor the perfect power $2^{4}$ out of $16$ .

$\sqrt[4]{\frac{{(x^{2})}^{4} x^{2}}{2^{4} \cdot 1}}$

Rearrange the fraction $\frac{{(x^{2})}^{4} x^{2}}{2^{4} \cdot 1}$ .

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

Pull terms out from under the radical.

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

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

$\frac{x^{2}}{2} \sqrt{\sqrt{x^{2}}}$

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

$\frac{x^{2}}{2} \sqrt{x}$

Combine $\frac{x^{2}}{2}$ and $\sqrt{x}$ .

$\frac{x^{2} \sqrt{x}}{2}$