Solve for x: 4^(2x-2) * 4^(-4x+1) = 1/16

This problem asks to solve for x in the equation 4^(2x-2) * 4^(-4x+1) = 1/16. The solution is x = 1/2.

Answer

Let’s solve this step by step:

First, let’s simplify the left side of the equation using the laws of exponents:
Now our equation looks like this:
We know that (because )
So we can rewrite our equation as:
When the bases are the same, the exponents must be equal for the equation to hold:
Now we can solve for x:

Therefore, the solution is:

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Solve for x: 4^(2x-2) * 4^(-4x+1) = 1/16

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