The given expression is:

\[
\frac{1}{(-1)^{-(-1)}}
\]

Let's break it down step by step:

1. First, simplify the exponent \(-(-1)\). This becomes:
   \[
   -(-1) = 1
   \]

2. Now the expression becomes:
   \[
   \frac{1}{(-1)^1}
   \]

3. \((-1)^1\) is simply \(-1\), so the expression becomes:
   \[
   \frac{1}{-1}
   \]

4. \(\frac{1}{-1} = -1\).

Thus, the value of the expression is:

\[
\boxed{-1}
\]

Would you like further details or have any questions?

Here are some related questions you might explore:
1. How do negative exponents work in general?
2. What is the rule for simplifying powers of negative numbers?
3. What is the difference between \((-1)^n\) and \(-1^n\)?
4. How do reciprocal and negative exponents relate?
5. Can you apply these rules to a similar problem, like \(\frac{1}{(-2)^{-2}}\)?

**Tip:** Always remember that negative exponents represent the reciprocal of the base raised to the corresponding positive exponent.

Learn how to simplify the expression 1/(-1)^-(-1) with a clear step-by-step solution. This problem covers key concepts such as negative exponents, reciprocal rules, and powers of negative numbers. Suitable for students in Grades 8-10.

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