Let's simplify the expression step by step:

The expression is:

[ \left[ \left( \frac{-1}{3} \right)^2 \right]^{-4} \right]^{-1} ]

Step 1: Simplify $\left( \frac{-1}{3} \right)^2$

$\left( \frac{-1}{3} \right)^2 = \frac{(-1)^2}{3^2} = \frac{1}{9}$

Step 2: Apply the exponent $-4$ to $\frac{1}{9}$

$\left( \frac{1}{9} \right)^{-4} = \left( \frac{9}{1} \right)^4 = 9^4$

Now, calculate $9^4$:

$9^4 = 9 \times 9 \times 9 \times 9 = 6561$

So, $\left( \frac{1}{9} \right)^{-4} = 6561$.

Step 3: Apply the outer exponent $-1$

$\left( 6561 \right)^{-1} = \frac{1}{6561}$

Thus, the simplified expression is:

$\boxed{\frac{1}{6561}}$

This is already expressed as a positive power.

Would you like any further explanation or more details on any step?

Here are 5 related questions you might find interesting:

1. How do you simplify expressions with negative exponents?
2. What is the rule for raising a fraction to a power?
3. How do you simplify nested exponents?
4. What is the difference between positive and negative powers in an expression?
5. Can you simplify $\left( \frac{a}{b} \right)^{-n}$ for any values of $a$, $b$, and $n$?

Tip: Always apply exponents in the correct order, starting from the innermost parentheses when dealing with nested powers.