  We investigate {\bf explicit} universal estimate of finite Morse index
solutions to polyharmonic equations. \,Differently to previous works \cite{BL2,
DDF, fa, H1}, propose here a direct proof using a new interpolation inequality
and a delicate boot-strap argument under large superlinear and subcritical
growth conditions to show that the universal constant grows as a power function
of the Morse index.\, Also, our interpolation inequality allows us to provide
local $L^p$-$W^{2r,p}$ estimate.
