Simplify 3y^2 fourth root of x^4z-x fourth root of 16y^8z

$3 y^{2} \sqrt[4]{x^{4} z} - x \sqrt[4]{16 y^{8} z}$

Step 1

Simplify each term.

Pull terms out from under the radical.

$3 y^{2} (x \sqrt[4]{z}) - x \sqrt[4]{16 y^{8} z}$

Rewrite $16 y^{8} z$ as ${(2 y^{2})}^{4} z$ .

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

$3 y^{2} x \sqrt[4]{z} - x \sqrt[4]{2^{4} y^{8} z}$

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

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

Step 2

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

Move $y^{2}$ .

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

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

$1 x y^{2} \sqrt[4]{z}$

Step 3

Multiply $x$ by $1$ .

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