https://file.aiquickdraw.com/mathbot/file/1727066128660wqeg921f.jpg

The equation in the image is:

\[
(2)^{3x+2} = 256
\]

To solve this equation, follow these steps:

### Step 1: Express 256 as a power of 2.
We know that:
\[
256 = 2^8
\]

Thus, the equation becomes:
\[
(2)^{3x+2} = 2^8
\]

### Step 2: Since the bases are the same, set the exponents equal to each other.
\[
3x + 2 = 8
\]

### Step 3: Solve for \(x\).
Subtract 2 from both sides:
\[
3x = 8 - 2
\]
\[
3x = 6
\]

Now, divide both sides by 3:
\[
x = \frac{6}{3} = 2
\]

### Final Answer:
\[
x = 2
\]

Would you like further clarification on any step or more details?

Here are some related questions for further practice:
1. Solve \( (3)^{x+1} = 27 \).
2. If \( (5)^{2x+1} = 125 \), find \(x\).
3. Solve \( (2)^{4x - 3} = 64 \).
4. If \( (4)^{x+2} = 1024 \), what is \(x\)?
5. Solve \( (3)^{2x+5} = 243 \).

**Tip:** When solving exponential equations, it often helps to express both sides as powers of the same base before comparing exponents.

Learn how to solve the exponential equation (2)^{3x+2} = 256 step by step. This problem covers exponential rules and algebraic techniques. Suitable for students in Grades 8-10.

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