One helpful way to calculate $a^{-m/n}$ is:

• Negative sign: take the reciprocal.
• Denominator $n$: take the $n$th root.
• Numerator $m$: raise to the power $m$.

So

$$a^{-m/n}=\frac{1}{(\sqrt[n]{a}{)}^m}=\frac{1}{\sqrt[n]{a^m}}$$

Example:

$$32^{-2/5}=\frac{1}{(\sqrt[5]{32}{)}^2}=\frac{1}{2^2}=\frac{1}{4}$$