https://file.aiquickdraw.com/mathbot/file/1728687776447o2rdkbat.jpg

We are given the equation:

\[
(6^n)^4 = 6^{-12}
\]

### Step 1: Simplify the left side
Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify the left-hand side:

\[
(6^n)^4 = 6^{4n}
\]

Now, the equation becomes:

\[
6^{4n} = 6^{-12}
\]

### Step 2: Set the exponents equal to each other
Since the bases are the same (both are base 6), we can set the exponents equal to each other:

\[
4n = -12
\]

### Step 3: Solve for \(n\)
Now, divide both sides by 4 to isolate \(n\):

\[
n = \frac{-12}{4} = -3
\]

Thus, the value of \(n\) is \(-3\).

The correct answer is \( \boxed{B} \).

---

Would you like further details or explanations? 

Here are 5 related questions:
1. How would the equation change if the base was different?
2. What are the key properties of exponents used in this problem?
3. How do you solve equations with negative exponents?
4. What happens if the exponents are fractions instead of integers?
5. Can you solve the equation without setting the exponents equal?

**Tip:** Remember that when dealing with exponential equations, if the bases are the same, you can simply compare the exponents directly!

An equation is shown. (6^n)^4 = 6^{-12}. What is the value of n?

Learn how to solve the exponential equation (6^n)^4 = 6^{-12} by using the power of a power rule and comparing exponents. This problem focuses on simplifying exponential expressions and is suitable for students in Grades 8-10.

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