  In this paper, we compute the Joseph-Lundgren exponent for the quadharmonic
Lane-Emden equation, derive a monotonicity formula and classify the finite
Morse index solution to the following quadharmonic Lane-Emden equation:
\noindent \begin{equation}\nonumber \Delta^4
u=|u|^{p-1}u\;\;\;\;\hbox{in}\;\;\;\;\; \R^n. \end{equation} As a byproduct, we
also get a monotonicity formula for the quadharmonic maps $ \Delta^4 u=0$.
