$\left (\left |x\right | - \frac{1}{8}\right ) \cdot \left (-{\frac{1}{8}}\right )^{5} = \left (-{\frac{1}{8}}\right )^{7}$
$\left (\left |x\right | - \dfrac{1}{8}\right ) \cdot \left (-{\dfrac{1}{8}}\right )^{5} = \left (-{\dfrac{1}{8}}\right )^{7}
\\\Leftrightarrow |x|-\dfrac{1}{8}=\left ( -\dfrac{1}{8} \right )^7:\left ( -\dfrac{1}{8} \right )^5
\\\Leftrightarrow |x|-\dfrac{1}{8}=\left ( -\dfrac{1}{8} \right )^2=\dfrac{1}{64}
\\\Leftrightarrow |x|=\dfrac{1}{64}+\dfrac{1}{8}=\dfrac{9}{64}
\\\Leftrightarrow x=\pm \dfrac{9}{64}$