https://file.aiquickdraw.com/mathbot/file/1727181994847a123rbs4.jpg

The expression given in the image is:

\[
\frac{(9)^{-4}}{(-3)^{-8}}
\]

We will simplify this expression step by step:

### Step 1: Rewrite the terms with negative exponents
Recall that \( a^{-n} = \frac{1}{a^n} \). So, the terms can be rewritten as:
\[
(9)^{-4} = \frac{1}{9^4}, \quad (-3)^{-8} = \frac{1}{(-3)^8}
\]

The entire expression now becomes:
\[
\frac{\frac{1}{9^4}}{\frac{1}{(-3)^8}} = \frac{1}{9^4} \times (-3)^8
\]

### Step 2: Simplify powers
Now calculate the powers:
- \( 9^4 = (3^2)^4 = 3^8 \), so \( 9^4 = 3^8 \)
- \( (-3)^8 = 3^8 \), because raising a negative number to an even power results in a positive number.

The expression now simplifies to:
\[
\frac{1}{3^8} \times 3^8 = 1
\]

### Final Answer:
The expression simplifies to \( 1 \), so the correct answer is:

\[
\boxed{A}
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the rule for handling negative exponents?
2. How do we simplify expressions with exponents and fractions?
3. What happens when we raise a negative base to an even power?
4. How do we combine powers with the same base in multiplication and division?
5. What is the difference between positive and negative exponents?

**Tip**: When simplifying fractions with exponents, always look for common bases to make calculations easier!

Which option is equivalent to (9)^(-4) / (-3)^(-8)?

Learn how to simplify the expression (9)^(-4) / (-3)^(-8) step-by-step using properties of exponents and exponent rules. This math problem is suitable for students in grades 8-10.

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