Simplify fourth root of 80x^10

$\sqrt[4]{80 x^{10}}$

Step 1

Rewrite $80 x^{10}$ as ${(2 x^{2})}^{4} \cdot (5 x^{2})$ .

Factor $16$ out of $80$ .

$\sqrt[4]{16 (5) x^{10}}$

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

$\sqrt[4]{2^{4} \cdot 5 x^{10}}$

Factor out $x^{8}$ .

$\sqrt[4]{2^{4} \cdot 5 (x^{8} x^{2})}$

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

$\sqrt[4]{2^{4} \cdot 5 ({(x^{2})}^{4} x^{2})}$

Move $5$ .

$\sqrt[4]{2^{4} {(x^{2})}^{4} \cdot 5 x^{2}}$

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

$\sqrt[4]{{(2 x^{2})}^{4} \cdot 5 x^{2}}$

Add parentheses.

$\sqrt[4]{{(2 x^{2})}^{4} \cdot (5 x^{2})}$

Step 2

Pull terms out from under the radical.

$2 x^{2} \sqrt[4]{5 x^{2}}$