Let's break down the expression step by step:

$9 + (9 - 8 + 3)^4$

Step 1: Simplify inside the parentheses first.

$9 - 8 + 3 = 4$

Now the expression becomes: $9 + 4^4$

Step 2: Calculate $4^4$.

$4^4 = 4 \times 4 \times 4 \times 4 = 256$

Step 3: Add 9 to the result.

$9 + 256 = 265$

So, the final answer is: $\boxed{265}$

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. What is the value of $(5 + 2)^3$?
2. How do you simplify expressions involving exponents?
3. What happens when we multiply two exponents with the same base?
4. How do parentheses affect the order of operations in complex expressions?
5. Can you solve $7 + (6 \times 2)^3$?

Tip: Always remember to handle operations inside parentheses first according to the order of operations (PEMDAS).