1. Evaluate the expression $\left(\frac{3}{5}\right)^{-4}$. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$. 3. Apply the rule: $$\left(\frac{3}{5}\right)^{-4} = \frac{1}{\left(\frac{3}{5}\right)^4} = \frac{1}{\frac{3^4}{5^4}} = \frac{1}{\frac{81}{625}} = \frac{625}{81}.$$ 4. Simplify the fraction if needed. Here, $\frac{625}{81}$ is already in simplest form. 5. Therefore, the value of $\left(\frac{3}{5}\right)^{-4}$ is $\frac{625}{81}$.