Rewrite $\left(\frac{-1}{5}\right)^{8}$ as $\left(\frac{-1}{5}\right)^{3}\times \left(\frac{-1}{5}\right)^{5}$. Cancel out $\left(\frac{-1}{5}\right)^{3}$ in both numerator and denominator.
$$\frac{1}{\left(\frac{-1}{5}\right)^{5}}$$
Fraction $\frac{-1}{5}$ can be rewritten as $-\frac{1}{5}$ by extracting the negative sign.
$$\frac{1}{\left(-\frac{1}{5}\right)^{5}}$$
Calculate $-\frac{1}{5}$ to the power of $5$ and get $-\frac{1}{3125}$.
$$\frac{1}{-\frac{1}{3125}}$$
Divide $1$ by $-\frac{1}{3125}$ by multiplying $1$ by the reciprocal of $-\frac{1}{3125}$.
