Simplify the Radical Expression square root of 7xy^18

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

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

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

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

Move $x$ .

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

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

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

$| y^{3^{2}} | \sqrt{7 x}$

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

$| y^{9} | \sqrt{7 x}$