Question

If 4^x=256 then 4^-x=?​

Answer 1

$4 ^{x} = 256 \\ 2 ^{2x} = 2 ^{8} \\ 2x = 8 \\ x = 4 \\now \\ = 4 ^{ - x} \\ = 4 ^{ - 4} \\ = (\frac{1}{4} ) ^{4} \\ = \frac{1}{256}$

Answer 2

Answer:

$\frac{1}{256}$

Step-by-step explanation:

$Given - \\ {4}^{x} = 256 \\ \\ {4}^{x} = {4}^{4} \\ \\ then \\ \\ x = 4 \\ \\ then \: the \: value \: of \: {4}^{ - x} \\ \\ = {4}^{ - 4} \: (putting \: x = - 4) \\ \\ = \frac{1}{4^{4}}\\ \\ = \frac{1}{256}$