$\left | a \right | = b^{2006}$
$\Leftrightarrow a = -b^{2006}$
$\Leftrightarrow -a = b^{2006}$
$\to \left[ \begin{array}{l}\left\{\begin{matrix}a < 0\\b > 0\end{matrix}\right.\\\left\{\begin{matrix}a > 0\\b < 0\end{matrix}\right.\end{array} \right.$