To solve $\left(\frac{4}{5}\right)^{-4}$, we apply the negative exponent rule, which states that:

$a^{-n} = \frac{1}{a^n}$

Thus, the expression becomes:

$\left(\frac{4}{5}\right)^{-4} = \frac{1}{\left(\frac{4}{5}\right)^4}$

Now, raise $\frac{4}{5}$ to the power of 4:

$\left(\frac{4}{5}\right)^4 = \frac{4^4}{5^4} = \frac{256}{625}$

Therefore:

$\left(\frac{4}{5}\right)^{-4} = \frac{1}{\frac{256}{625}} = \frac{625}{256}$

So, the final result is:

$\left(\frac{4}{5}\right)^{-4} = \frac{625}{256}$

Would you like more details or have any questions?

Here are some related questions:

1. What is the value of $\left(\frac{3}{7}\right)^{-3}$?
2. How do you simplify $2^{-5}$?
3. What is the general formula for negative exponents?
4. How do you simplify $\left(\frac{6}{7}\right)^{2}$?
5. What is $\left(\frac{7}{3}\right)^{-2}$?

Tip: When dealing with negative exponents, always flip the base and apply the positive exponent.