Simplify sixth root of 1/(w^-6*w^4)

$\sqrt[6]{\frac{1}{w^{- 6} \cdot w^{4}}}$

Multiply $w^{- 6}$ by $w^{4}$ by adding the exponents.

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

$\sqrt[6]{\frac{1}{w^{- 6 + 4}}}$

Add $- 6$ and $4$ .

$\sqrt[6]{\frac{1}{w^{- 2}}}$

Move $w^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Rewrite $\sqrt[6]{w^{2}}$ as $\sqrt[3]{\sqrt{w^{2}}}$ .

$\sqrt[3]{\sqrt{w^{2}}}$

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

$\sqrt[3]{w}$