Rewrite $\left(\frac{-2}{9}\right)^{-3}$ as $\left(\frac{-2}{9}\right)^{-5}\times \left(\frac{-2}{9}\right)^{2}$. Cancel out $\left(\frac{-2}{9}\right)^{-5}$ in both numerator and denominator.
$$\frac{1}{\left(\frac{-2}{9}\right)^{2}}$$
Fraction $\frac{-2}{9}$ can be rewritten as $-\frac{2}{9}$ by extracting the negative sign.
$$\frac{1}{\left(-\frac{2}{9}\right)^{2}}$$
Calculate $-\frac{2}{9}$ to the power of $2$ and get $\frac{4}{81}$.
$$\frac{1}{\frac{4}{81}}$$
Divide $1$ by $\frac{4}{81}$ by multiplying $1$ by the reciprocal of $\frac{4}{81}$.
$$1\times \frac{81}{4}$$
Multiply $1$ and $\frac{81}{4}$ to get $\frac{81}{4}$.
