https://file.aiquickdraw.com/mathbot/file/1727934301260oah1timb.jpg

The expression shown in the image is:

\[
3^2 \cdot 3^{-5}
\]

To simplify this, we use the property of exponents that states:

\[
a^m \cdot a^n = a^{m+n}
\]

Here, both terms have the same base (3), so we can add the exponents:

\[
3^2 \cdot 3^{-5} = 3^{2 + (-5)} = 3^{-3}
\]

Now, \( 3^{-3} \) can be written as:

\[
\frac{1}{3^3} = \frac{1}{27}
\]

Thus, the simplified result is:

\[
\frac{1}{27}
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What happens if the base is different, but the exponents are the same?
2. How do we handle negative exponents in other expressions?
3. Can you simplify \(2^3 \cdot 2^{-4}\)?
4. What is the general rule for dividing terms with the same base and exponents?
5. How do fractional exponents work when simplifying?

**Tip:** Always check if bases are the same when multiplying or dividing terms with exponents, as it allows for easy simplification!

Learn how to simplify the expression 3^2 * 3^(-5) using exponent rules. This guide covers key concepts such as exponent addition and handling negative exponents. Suitable for students in Grades 6-8.

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