Simplify the Radical Expression fourth root of x^5y^9z^6

$\sqrt[4]{x^{5} y^{9} z^{6}}$

Step 1

Rewrite $x^{5} y^{9} z^{6}$ as ${(x y^{2} z)}^{4} (x y z^{2})$ .

Factor out $x^{4}$ .

$\sqrt[4]{x^{4} x y^{9} z^{6}}$

Factor out $y^{8}$ .

$\sqrt[4]{x^{4} x (y^{8} y) z^{6}}$

Rewrite $y^{8}$ as ${(y^{2})}^{4}$ .

$\sqrt[4]{x^{4} x ({(y^{2})}^{4} y) z^{6}}$

Factor out $z^{4}$ .

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

Move $y$ .

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

Move $x$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$| x y^{2} z | \sqrt[4]{x y z^{2}}$

Step 3

Remove non-negative terms from the absolute value.

$y^{2} | x z | \sqrt[4]{x y z^{2}}$