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.

Learn how to solve the expression (4/5)^-4 using the negative exponent rule. This solution demonstrates key exponent concepts, including the process of flipping the fraction and raising it to a positive power. Suitable for students in Grades 8-10.

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