Simplify square root of 14x^14z

$\sqrt{14 x^{14} z}$

Rewrite $14 x^{14} z$ as ${(x^{7})}^{2} \cdot (14 z)$ .

Rewrite $x^{14}$ as ${(x^{7})}^{2}$ .

$\sqrt{14 {(x^{7})}^{2} z}$

Reorder $14$ and ${(x^{7})}^{2}$ .

$\sqrt{{(x^{7})}^{2} \cdot 14 z}$

Add parentheses.

$\sqrt{{(x^{7})}^{2} \cdot (14 z)}$

Pull terms out from under the radical.

$x^{7} \sqrt{14 z}$