The expression in the image appears to be:

$\left( -7^{-2} \right)^{-1}.$

Let's solve this step by step:

Step 1: Simplify the inner exponent

The base is $-7$, and the exponent is $-2$. Using the rule for negative exponents $a^{-n} = \frac{1}{a^n}$, we have: $-7^{-2} = -\frac{1}{7^2}.$

Now calculate $7^2$: $7^2 = 49.$

Thus: $-7^{-2} = -\frac{1}{49}.$

Step 2: Apply the outer exponent

The outer exponent is $-1$. Again, use the negative exponent rule. Raising $-\frac{1}{49}$ to the power of $-1$ is equivalent to taking the reciprocal: $\left(-\frac{1}{49}\right)^{-1} = -49.$

Final Answer:

$\left( -7^{-2} \right)^{-1} = -49.$

Do you have any questions, or would you like further clarification?

Here are some related questions for further exploration:

1. What are the rules of exponents for negative bases?
2. How does the negative exponent rule apply to fractions?
3. Can negative bases have fractional exponents?
4. What happens if the outer exponent is even instead of odd?
5. How do parentheses affect operations with exponents?

Tip: Always simplify expressions inside parentheses first before applying outer operations!