To solve this equation, we need to use the property of exponents which states that (a^b)^c = a^(b*c).
Therefore, we can rewrite the given equation as:
(6^n)^4 = 6^(-12)
Now, using the property mentioned above, we can simplify the left side of the equation as follows:
6^(4*n) = 6^(-12)
Since the bases are the same on both sides, we can now equate the exponents:
4*n = -12
Dividing by 4 on both sides:
n = -3
Therefore, the solution to the equation (6^n)^4 = 6^(-12) is n = -3.
(6^n)^4=6^-12
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