Question

An equation is shown.



(6^n)^4 = 6-^12

What is the value of n?
Responses
A 33
B -3-3
C 22
D -2

Answer 1

To solve the equation \((6^n)^4 = 6^{-12}\), we can start by simplifying the left-hand side.

Using the property of exponents that states \((a^m)^n = a^{m \cdot n}\), we can rewrite the left side:

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

Now, the equation becomes:

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

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

\[
4n = -12
\]

Now, solving for \(n\) involves dividing both sides by 4:

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

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

Looking at the responses provided:

A: 33
B: -3
C: 22
D: -2

The correct response is **B: -3**.