Answer
Error: writing $\frac{1}{8}$ as $2^{3}$ instead of $2^{-3}$.
Correct solution is $x=-2$.
Work Step by Step
$\frac{1}{8}$ is $2^{-3}$. The error is to take it as $2^{3}
$.
Making this correction, we have
$(2^{-3})^{5x}=(2^{5})^{x+8}$
$\implies 2^{-15x}=2^{5x+40}$
Equating the exponents, we get
$ -15x=5x+40$
$\implies -15x-5x=40$
$x=\frac{40}{-20}=-2$
