1. The problem asks to evaluate $\left(\frac{4}{5}\right)^{-2}$.\n\n2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$. This means we take the reciprocal of the base and then raise it to the positive exponent.\n\n3. Applying this rule, we get:\n$$\left(\frac{4}{5}\right)^{-2} = \frac{1}{\left(\frac{4}{5}\right)^2}$$\n\n4. Next, calculate $\left(\frac{4}{5}\right)^2$ by squaring numerator and denominator:\n$$\left(\frac{4}{5}\right)^2 = \frac{4^2}{5^2} = \frac{16}{25}$$\n\n5. Substitute back into the expression:\n$$\frac{1}{\frac{16}{25}}$$\n\n6. Dividing by a fraction is the same as multiplying by its reciprocal:\n$$= 1 \times \frac{25}{16} = \frac{25}{16}$$\n\n7. Therefore, the value of $\left(\frac{4}{5}\right)^{-2}$ is $\frac{25}{16}$.\n\nAnswer: a) $\frac{25}{16}$