https://file.aiquickdraw.com/mathbot/file/1729527831176yi9oydo8.jpg

Let's solve the problem shown in the image.

The equation provided is:

\[
216 = 6^{(4x + 11)}
\]

We need to find the value of \( x \). Here's how we can solve it:

### Step-by-Step Solution:

1. **Express 216 as a power of 6:**
   - We know \( 216 = 6^3 \).
   
   So, the equation becomes:
   \[
   6^3 = 6^{(4x + 11)}
   \]

2. **Equate the exponents:**
   Since the bases are the same, we can set the exponents equal to each other:
   \[
   3 = 4x + 11
   \]

3. **Solve for \( x \):**
   \[
   3 - 11 = 4x
   \]
   \[
   -8 = 4x
   \]
   \[
   x = \frac{-8}{4} = -2
   \]

Therefore, the correct answer is:

\[
\boxed{x = -2}
\]

### Conclusion:
The correct option is **A. \( x = -2 \)**.

Would you like further details or have any questions?

### Related Questions:
1. How do you solve exponential equations with different bases?
2. What are the properties of exponents that can simplify such equations?
3. How would the solution change if the equation were \( 216 = 6^{(2x + 5)} \)?
4. How can you check your solution to ensure it is correct?
5. What are some common mistakes to avoid when solving exponential equations?

### Tip:
When solving exponential equations, try to express both sides of the equation as powers of the same base to simplify the problem.

Solve the exponential equation for x: 216 = 6^(4x + 11).

Learn how to solve the exponential equation 216 = 6^(4x + 11) step by step. This solution involves understanding properties of exponents and algebraic manipulation to find the value of x. Suitable for high school students in Grades 9-11.

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