Simplify square root of 14xz^18

$\sqrt{14 x z^{18}}$

Step 1

Rewrite $14 x z^{18}$ as ${(z^{3^{2}})}^{2} \cdot (14 x)$ .

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

$\sqrt{14 x {(z^{9})}^{2}}$

Move $x$ .

$\sqrt{14 {(z^{9})}^{2} x}$

Reorder $14$ and ${(z^{9})}^{2}$ .

$\sqrt{{(z^{9})}^{2} \cdot 14 x}$

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

$\sqrt{{(z^{3^{2}})}^{2} \cdot 14 x}$

Add parentheses.

$\sqrt{{(z^{3^{2}})}^{2} \cdot (14 x)}$

Step 2

Pull terms out from under the radical.

$z^{3^{2}} \sqrt{14 x}$

Step 3

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

$z^{9} \sqrt{14 x}$