Simplify square root of 10xy^14

$\sqrt{10 x y^{14}}$

Rewrite $10 x y^{14}$ as ${(y^{7})}^{2} \cdot (10 x)$ .

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

$\sqrt{10 x {(y^{7})}^{2}}$

Move $x$ .

$\sqrt{10 {(y^{7})}^{2} x}$

Reorder $10$ and ${(y^{7})}^{2}$ .

$\sqrt{{(y^{7})}^{2} \cdot 10 x}$

Add parentheses.

$\sqrt{{(y^{7})}^{2} \cdot (10 x)}$

Pull terms out from under the radical.

$y^{7} \sqrt{10 x}$