Explanation

4^(4x+1) = 1/64

We can start by noticing that 1/64 = 2^(-6) = 4^(-3) (since 4 = 2^2).

So, we have:

4^(4x+1) = 4^(-3)

Since the bases are the same (both are 4), we can equate the exponents:

4x + 1 = -3

Subtracting 1 from both sides gives:

4x = -4

Dividing both sides by -4 gives:

x = -1