Simplify ( square root of x^4y^2z)(y^2z)

$(\sqrt{x^{4} y^{2} z}) (y^{2} z)$

Rewrite $x^{4} y^{2} z$ as ${(x^{2} y)}^{2} z$ .

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{{(x^{2})}^{2} y^{2} z} (y^{2} z)$

Rewrite ${(x^{2})}^{2} y^{2}$ as ${(x^{2} y)}^{2}$ .

$\sqrt{{(x^{2} y)}^{2} z} (y^{2} z)$

Pull terms out from under the radical.

$x^{2} y \sqrt{z} (y^{2} z)$

Multiply $y$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$x^{2} (y^{2} y) \sqrt{z} z$

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

$x^{2} (y^{2} y^{1}) \sqrt{z} z$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} y^{2 + 1} \sqrt{z} z$

Add $2$ and $1$ .

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