https://r2.erweima.ai/mathbot/image/1726575295857a77wmgj1.jpg

The mathematical expression shown in the image is:

\[
(3^5) \times (3^4)^2 \div (3^3)^5
\]

### Steps to simplify:

1. **Simplify the second term**:
   \[
   (3^4)^2 = 3^{4 \times 2} = 3^8
   \]
   So the expression becomes:
   \[
   3^5 \times 3^8 \div (3^3)^5
   \]

2. **Simplify the denominator**:
   \[
   (3^3)^5 = 3^{3 \times 5} = 3^{15}
   \]
   Now, the expression is:
   \[
   3^5 \times 3^8 \div 3^{15}
   \]

3. **Combine the exponents in the numerator**:
   \[
   3^5 \times 3^8 = 3^{5+8} = 3^{13}
   \]
   The expression is now:
   \[
   3^{13} \div 3^{15}
   \]

4. **Simplify the final division** (subtract the exponents):
   \[
   3^{13} \div 3^{15} = 3^{13 - 15} = 3^{-2}
   \]

Thus, the simplified expression is:

\[
3^{-2}
\]

Alternatively, this can be written as:

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

Would you like more details or explanations on any part of this solution?

Here are 5 related questions for further exploration:
1. How do you handle negative exponents in expressions?
2. What happens when you divide two powers with the same base but different exponents?
3. Can you simplify \((2^3 \times 2^5) \div (2^4)^2\)?
4. What is the general rule for simplifying expressions like \((a^b)^c\)?
5. How do you simplify expressions with different bases but similar operations?

**Tip**: When multiplying or dividing exponents with the same base, you can simply add or subtract the exponents respectively!

Learn how to simplify the exponent expression (3^5) x (3^4)^2 ÷ (3^3)^5 step-by-step. This problem introduces key concepts in algebra and exponentiation, focusing on simplifying powers and dividing exponents.

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