https://file.aiquickdraw.com/mathbot/file/172654309031860rexh7e.jpg

The expression shown in the image is:

\[
\frac{1}{3^{-2}}
\]

To simplify this:

1. First, recall the property of exponents that states \( a^{-n} = \frac{1}{a^n} \). Applying this to the denominator \( 3^{-2} \), we get:

\[
3^{-2} = \frac{1}{3^2} = \frac{1}{9}
\]

2. Now, substitute this into the original expression:

\[
\frac{1}{\frac{1}{9}} = 9
\]

Thus, the simplified expression is:

\[
9
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you simplify expressions with negative exponents in the numerator?
2. What is the general rule for multiplying powers with the same base?
3. How do you handle fractions with exponents in both the numerator and denominator?
4. Can you simplify an expression like \( \frac{2^3}{2^{-4}} \)?
5. How do negative exponents apply to variables instead of numbers?

**Tip:** When working with negative exponents, remember that they indicate the reciprocal of the base raised to the positive exponent.

Learn how to simplify the expression 1 / 3^(-2) by applying the rules of exponents. This problem demonstrates how negative exponents represent reciprocals. Ideal for students in Grades 7-9.

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