Simplify the expression: ((-(2)/(3))⁻²)⁻²

The expression shown is a power raised to another power:

$$\left\{\left(-\frac{2}{3}\right)^{-2}\right\}^{-2}$$

In this case, $a = \left(-\frac{2}{3}\right)$, $m = -2$, and $n = -2$.

$$\left(-\frac{2}{3}\right)^{(-2) \times (-2)}$$

When a fraction is raised to a power, both the numerator and the denominator are raised to that power. A negative base raised to an even power results in a positive value.

$$\frac{(-2)^4}{(3)^4}$$

$$(-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16$$ $$(3)^4 = 3 \times 3 \times 3 \times 3 = 81$$