Simplify fourth root of 16w^10+2w fourth root of w^6

$\sqrt[4]{16 w^{10}} + 2 w \sqrt[4]{w^{6}}$

Step 1

Simplify each term.

Rewrite $16 w^{10}$ as ${(2 w^{2})}^{4} w^{2}$ .

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

$\sqrt[4]{2^{4} w^{10}} + 2 w \sqrt[4]{w^{6}}$

Factor out $w^{8}$ .

$\sqrt[4]{2^{4} (w^{8} w^{2})} + 2 w \sqrt[4]{w^{6}}$

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

$\sqrt[4]{2^{4} ({(w^{2})}^{4} w^{2})} + 2 w \sqrt[4]{w^{6}}$

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

$\sqrt[4]{{(2 w^{2})}^{4} w^{2}} + 2 w \sqrt[4]{w^{6}}$

Pull terms out from under the radical.

$2 w^{2} \sqrt[4]{w^{2}} + 2 w \sqrt[4]{w^{6}}$

Rewrite $\sqrt[4]{w^{2}}$ as $\sqrt{\sqrt{w^{2}}}$ .

$2 w^{2} \sqrt{\sqrt{w^{2}}} + 2 w \sqrt[4]{w^{6}}$

Pull terms out from under the radical, assuming positive real numbers.

$2 w^{2} \sqrt{w} + 2 w \sqrt[4]{w^{6}}$

Factor out $w^{4}$ .

$2 w^{2} \sqrt{w} + 2 w \sqrt[4]{w^{4} w^{2}}$

Pull terms out from under the radical.

$2 w^{2} \sqrt{w} + 2 w (w \sqrt[4]{w^{2}})$

Multiply $w$ by $w$ by adding the exponents.

Move $w$ .

$2 w^{2} \sqrt{w} + 2 (w \cdot w) \sqrt[4]{w^{2}}$

Multiply $w$ by $w$ .

$2 w^{2} \sqrt{w} + 2 w^{2} \sqrt[4]{w^{2}}$

Rewrite $\sqrt[4]{w^{2}}$ as $\sqrt{\sqrt{w^{2}}}$ .

$2 w^{2} \sqrt{w} + 2 w^{2} \sqrt{\sqrt{w^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$2 w^{2} \sqrt{w} + 2 w^{2} \sqrt{w}$

Step 2

Add $2 w^{2} \sqrt{w}$ and $2 w^{2} \sqrt{w}$ .

$4 w^{2} \sqrt{w}$