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Let's solve the expression \( 3^4 \div 3^9 \) and identify which of the given options are correct.

### Step 1: Apply the Law of Exponents
When dividing powers with the same base, we subtract the exponents:
\[
3^4 \div 3^9 = 3^{4 - 9} = 3^{-5}
\]

### Step 2: Simplify Further
\[
3^{-5} = \frac{1}{3^5}
\]

### Step 3: Compare with the Given Options

- \( 3^{13} \): Incorrect.
- \( 3^5 \): Incorrect.
- \( \frac{1}{243} \): Correct. Since \( 3^5 = 243 \), \( \frac{1}{3^5} = \frac{1}{243} \).
- \( \frac{1}{3^5} \): Correct. This directly matches the simplified expression.
- \( 1^5 \): Incorrect.

### Correct Answers
- \( \frac{1}{243} \)
- \( \frac{1}{3^5} \)

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the rule for multiplying powers with the same base?
2. How do you simplify expressions with negative exponents?
3. Can you simplify \( \frac{1}{3^{-3}} \)?
4. What is the value of \( 3^5 \)?
5. How would you simplify \( 2^4 \div 2^6 \)?

**Tip:** When dividing powers with the same base, always subtract the exponents.

Select all simplified expressions of 3^4 ÷ 3^9.

Learn how to simplify the expression 3^4 ÷ 3^9 using exponent rules. This problem covers key concepts like division of powers and negative exponents, suitable for students in Grades 8-10. Discover the correct simplified forms and understand the laws of exponents with step-by-step guidance.

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