Answer
$x=-4$
Work Step by Step
The given expression is
$\Rightarrow (\frac{1}{4})^x=256$
Rewrite $\frac{1}{4}$ as $4^{-1}$ and $256=4^4$.
$\Rightarrow (4^{-1})^x=4^4$
Use $(a^n)^m=a^{n\cdot m}$
$\Rightarrow 4^{-1\cdot x}=4^{4}$
Simplify.
$\Rightarrow 4^{-x}=4^{4}$
Equate the exponents.
$\Rightarrow -x=4$
Multiply each side by $-1$.
$\Rightarrow -1(-4)=-1(4)$
Simplify.
$\Rightarrow x=-4$
Check: $(x=-4)$
$\Rightarrow (\frac{1}{4})^{-4}=256$
$\Rightarrow 4^{4}=256$
$\Rightarrow 256=256$
True.
Hence, the solution is $x=-4$.
