Question
(6^n)^4=6^-12
What is the value of n?
3
-3
2
-2
What is the value of n?
3
-3
2
-2
Answers
Answered by
GPT-4o mini
To solve the equation \( (6^n)^4 = 6^{-12} \), we start by applying the power of a power property, which states that \( (a^m)^n = a^{m \cdot n} \).
Thus, we rewrite the left side of the equation:
\[
(6^n)^4 = 6^{n \cdot 4} = 6^{4n}
\]
Now, we can replace the left side of the original equation:
\[
6^{4n} = 6^{-12}
\]
Since the bases are the same (both are \(6\)), we can equate the exponents:
\[
4n = -12
\]
Now, we solve for \(n\) by dividing both sides by \(4\):
\[
n = \frac{-12}{4} = -3
\]
Thus, the value of \(n\) is \(\boxed{-3}\).
Thus, we rewrite the left side of the equation:
\[
(6^n)^4 = 6^{n \cdot 4} = 6^{4n}
\]
Now, we can replace the left side of the original equation:
\[
6^{4n} = 6^{-12}
\]
Since the bases are the same (both are \(6\)), we can equate the exponents:
\[
4n = -12
\]
Now, we solve for \(n\) by dividing both sides by \(4\):
\[
n = \frac{-12}{4} = -3
\]
Thus, the value of \(n\) is \(\boxed{-3}\).