Simplify fourth root of w square root of w

$\sqrt[4]{w} \sqrt{w}$

Step 1

Rewrite the expression using the least common index of $4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{w}$ as $w^{\frac{1}{2}}$ .

$\sqrt[4]{w} w^{\frac{1}{2}}$

Rewrite $w^{\frac{1}{2}}$ as $w^{\frac{2}{4}}$ .

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

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

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

Step 2

Combine using the product rule for radicals.

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

Step 3

Multiply $w$ by $w^{2}$ by adding the exponents.

Multiply $w$ by $w^{2}$ .

Raise $w$ to the power of $1$ .

$\sqrt[4]{w^{1} w^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[4]{w^{1 + 2}}$

Add $1$ and $2$ .

$\sqrt[4]{w^{3}}$