Simplify fourth root of 48xy^11z^3

$\sqrt[4]{48 x y^{11} z^{3}}$

Rewrite $48 x y^{11} z^{3}$ as ${(2 y^{2})}^{4} \cdot (3 x y^{3} z^{3})$ .

Factor $16$ out of $48$ .

$\sqrt[4]{16 (3) x y^{11} z^{3}}$

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} \cdot 3 x y^{11} z^{3}}$

Factor out $y^{8}$ .

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

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

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

Move $x$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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