\sqrt{8}=\sqrt{2^3}=(2^3)^{\frac{1}{2}}=2^{\frac{3}{2}}
,
\frac{1}{\sqrt{8}}=4^{m-2}
\frac{1}{2^{\frac{2}{3}}}=2^{2(m-2)}
2^{-\frac{2}{3}}=2^{2m-4}
-\frac{2}{3}=2m-4 \ |*3
-2=4x-12
-4x=-12+2
-4x=-10 \ |:(-4)
x=\frac{-10}{-4}=\frac{5}{4}
x=1\frac{1}{4}