Answer
$x=-\dfrac{1}{5}$
Work Step by Step
RECALL:
(i) If $a^M=a^N$, then $M=N.$
(ii) $(a^m)^n=a^{mn}.$
Write 8 and 4 as powers of 2:
$8^{1-x} = 4^{x+2}
\\(2^3)^{1-x}=(2^2)^{x+2}.$
Use rule (ii) above to obtain
$2^{3(1-x)} = 2^{2(x+2)}
\\2^{3-3x} = 2^{2x+4}.$
Use rule (i) to obtain
$3-3x=2x+4.$
Solve the equation to obtain
$3-4=2x+3x
\\-1=5x
\\\dfrac{-1}{5}=x.$
