Simplify square root of 7xz^18

$\sqrt{7 x z^{18}}$

Rewrite $7 x z^{18}$ as ${(z^{3^{2}})}^{2} \cdot (7 x)$ .

Rewrite $z^{18}$ as ${(z^{9})}^{2}$ .

$\sqrt{7 x {(z^{9})}^{2}}$

Move $x$ .

$\sqrt{7 {(z^{9})}^{2} x}$

Reorder $7$ and ${(z^{9})}^{2}$ .

$\sqrt{{(z^{9})}^{2} \cdot 7 x}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{{(z^{3^{2}})}^{2} \cdot 7 x}$

Add parentheses.

$\sqrt{{(z^{3^{2}})}^{2} \cdot (7 x)}$

Pull terms out from under the radical.

$z^{3^{2}} \sqrt{7 x}$

Raise $3$ to the power of $2$ .

$z^{9} \sqrt{7 x}$