Simplify fourth root of 10x^5y^8z^10

$\sqrt[4]{10 x^{5} y^{8} z^{10}}$

Step 1

Rewrite $10 x^{5} y^{8} z^{10}$ as ${(x y^{2} z^{2})}^{4} \cdot (10 x z^{2})$ .

Factor out $x^{4}$ .

$\sqrt[4]{10 (x^{4} x) y^{8} z^{10}}$

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

$\sqrt[4]{10 (x^{4} x) {(y^{2})}^{4} z^{10}}$

Factor out $z^{8}$ .

$\sqrt[4]{10 (x^{4} x) {(y^{2})}^{4} (z^{8} z^{2})}$

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

$\sqrt[4]{10 (x^{4} x) {(y^{2})}^{4} ({(z^{2})}^{4} z^{2})}$

Move $x$ .

$\sqrt[4]{10 (x^{4}) {(y^{2})}^{4} {(z^{2})}^{4} x z^{2}}$

Move $10$ .

$\sqrt[4]{(x^{4}) {(y^{2})}^{4} {(z^{2})}^{4} \cdot 10 x z^{2}}$

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

$\sqrt[4]{{(x y^{2} z^{2})}^{4} \cdot 10 x z^{2}}$

Add parentheses.

$\sqrt[4]{{(x y^{2} z^{2})}^{4} \cdot 10 (x z^{2})}$

Add parentheses.

$\sqrt[4]{{(x y^{2} z^{2})}^{4} \cdot (10 x z^{2})}$

Step 2

Pull terms out from under the radical.

$x y^{2} z^{2} \sqrt[4]{10 x z^{2}}$