Question

What value of k solves the equation? k-4=1/256 A: 64 B: 4 C: -4 D: -64

Answer 1

$k^{-4}=\dfrac{1}{256}\\\\k^{-4}=\dfrac{1}{4^4}\\\\k^{-4}=4^{-4}\Rightarrow \boxed{k=4}\to\boxed{B.}\\\\\text{But k=-4 is solution too, because}:\\\\(-4)^{-4}=\dfrac{1}{(-4)^4}=\dfrac{1}{256}\\\\\text{Therefore the solution is 4 and -4}\to\boxed{B.\ and\ C.}\\\\Used:\\\\a^{-n}=\dfrac{1}{a^n}$

Answer 2

1/256 is 0.00390625

and you have to add 4 to both sides to get k by itself. So k is:

k = 4.00390625

So I would just put B