If you mean this: [tex] 4^{3x} = 1[/tex] then x = 0. The property in play here is the following: Any number raised to the "0" power is equal to "1". In this case, we would need to set the exponent of 3x = 0 and solve for x...
If you mean the equation: [tex] 4^{3} x = 1[/tex] then to solve for x(your blank), simply divide both sides of the equation by [tex] 4^{3} [/tex] :
You would have x = [tex] \frac{1}{4^3} [/tex] this can also be written as [tex] 4^{-3} [/tex]
