Simplify eighth root of w^3*w^-1

$\sqrt[8]{w^{3} \cdot w^{- 1}}$

Multiply $w^{3}$ by $w^{- 1}$ by adding the exponents.

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

$\sqrt[8]{w^{3 - 1}}$

Subtract $1$ from $3$ .

$\sqrt[8]{w^{2}}$

Rewrite $\sqrt[8]{w^{2}}$ as $\sqrt[4]{\sqrt{w^{2}}}$ .

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

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

$\sqrt[4]{w}$