  The existence of a linearized SUSY invariant for N=8 supergravity whose
gravitational components are usually called R^4 was established long ago by
on-shell superspace arguments. Superspace and string theory methods have also
established analogous higher dimensional D^{2k} R^4 invariants. However, very
little is known about the SUSY completions of these operators which involve
other fields of the theory. In this paper we find the detailed component
expansion of the linearized R^4 invariant starting from the corresponding
superamplitude which generates all component matrix elements of the operator.
It is then quite straightforward to extend results to the entire set of D^{2k}
R^4 operators.
