[{(-1/3)^2}^-4]^-1 simplify and express it as a positive power

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.

Simplify the expression [{(-1/3)^2}^-4]^-1 and express it as a positive power. This detailed step-by-step solution uses exponentiation rules, the negative power rule, and fractional exponent calculations. Suitable for students in Grades 9-10.

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