Simplify fourth root of 18x^8y^9z^3

$\sqrt[4]{18 x^{8} y^{9} z^{3}}$

Step 1

Rewrite $18 x^{8} y^{9} z^{3}$ as ${(x^{2} y^{2})}^{4} \cdot (18 y z^{3})$ .

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

$\sqrt[4]{18 {(x^{2})}^{4} y^{9} z^{3}}$

Factor out $y^{8}$ .

$\sqrt[4]{18 {(x^{2})}^{4} (y^{8} y) z^{3}}$

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

$\sqrt[4]{18 {(x^{2})}^{4} ({(y^{2})}^{4} y) z^{3}}$

Move $18$ .

$\sqrt[4]{{(x^{2})}^{4} {(y^{2})}^{4} \cdot 18 y z^{3}}$

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

$\sqrt[4]{{(x^{2} y^{2})}^{4} \cdot 18 y z^{3}}$

Add parentheses.

$\sqrt[4]{{(x^{2} y^{2})}^{4} \cdot 18 (y z^{3})}$

Add parentheses.

$\sqrt[4]{{(x^{2} y^{2})}^{4} \cdot (18 y z^{3})}$

Step 2

Pull terms out from under the radical.

$x^{2} y^{2} \sqrt[4]{18 y z^{3}}$