f. $\left(\frac{1}{4^{x}}\right)^{3}=4$

Step 1 ：The given equation is \(\left(\frac{1}{4^{x}}\right)^{3}=4\). To solve for x, we first need to simplify the equation. We can do this by taking the cube root of both sides and then taking the logarithm base 4 of both sides.

Step 2 ：The solution provided is in complex numbers. However, in the context of this problem, we are looking for real solutions. Among the solutions, -1/3 is a real number. Let's substitute x = -1/3 back into the original equation to verify if it is a valid solution.

Step 3 ：The result is very close to zero, which means x = -1/3 is indeed a solution to the equation.

Step 4 ：Final Answer: The solution to the equation \(\left(\frac{1}{4^{x}}\right)^{3}=4\) is \(\boxed{-\frac{1}{3}}\).