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

1 answer

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.