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The given expression is:

\[
2 \cdot 9^{-2} \div 9^{-4}
\]

### Step-by-step Solution:

1. **Apply the division of exponents rule**: 
   \[
   a^m \div a^n = a^{m-n}
   \]
   Here, we are dividing \( 9^{-2} \) by \( 9^{-4} \), so:

   \[
   9^{-2} \div 9^{-4} = 9^{-2 - (-4)} = 9^{-2 + 4} = 9^2
   \]

2. **Simplify the expression**:
   Now the expression becomes:
   \[
   2 \cdot 9^2
   \]

3. **Calculate \( 9^2 \)**:
   \[
   9^2 = 81
   \]

4. **Final multiplication**:
   \[
   2 \cdot 81 = 162
   \]

So, the value of the expression is:

\[
\boxed{162}
\]

Do you have any questions or would you like further clarification?

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Here are 5 related questions for practice:

1. Simplify \( 3 \cdot 5^{-1} \div 5^{-3} \).
2. What is the value of \( 2^4 \cdot 2^{-6} \)?
3. Simplify \( 10^{-2} \times 10^5 \).
4. How would you evaluate \( 8 \cdot 4^{-3} \div 4^{-1} \)?
5. Solve \( 6 \cdot 2^3 \div 2^5 \).

### Tip:
When dividing powers with the same base, subtract the exponents. When multiplying powers, add the exponents.

Learn how to simplify the expression 2 × 9^-2 ÷ 9^-4 using exponent rules. This step-by-step guide covers key concepts such as division of powers and calculating exponents. Perfect for students in Grades 7-9.

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