We are given the equation:

\[
3^{3x + 6} = \frac{1}{27}
\]

### Step 1: Rewrite the right-hand side with a base of 3.
We know that \( 27 = 3^3 \), so we can rewrite the equation as:

\[
\frac{1}{27} = 3^{-3}
\]

This simplifies the equation to:

\[
3^{3x + 6} = 3^{-3}
\]

### Step 2: Set the exponents equal.
Since the bases are the same, we can set the exponents equal to each other:

\[
3x + 6 = -3
\]

### Step 3: Solve for \(x\).
Now, solve for \(x\):

\[
3x + 6 = -3
\]

Subtract 6 from both sides:

\[
3x = -9
\]

Divide both sides by 3:

\[
x = -3
\]

Thus, the solution is \(x = -3\).

Would you like further clarification or details?

Here are 5 related questions:
1. How do you solve exponential equations with different bases?
2. What happens when exponents involve fractions?
3. Can logarithms help solve exponential equations?
4. How would you solve \(3^{2x+4} = 9\)?
5. How can you check if your solution to an exponential equation is correct?

**Tip**: Always try to express both sides of an exponential equation with the same base for easier comparison!

Discover how to solve the exponential equation 3^(3x+6) = 1/27 by converting the bases and setting exponents equal. This step-by-step guide is perfect for students in Grades 9-11, covering exponential rules and algebraic methods.

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