  In this study, we consider a flat Friedmann-Robertson-Walker (FRW) universe
in the context of Palatini $f(R)$ theory of gravity. Using the dynamical
equivalence between $f(R)$ gravity and scalar-tensor theories, we construct a
point Lagrangian in the flat FRW spacetime. Applying {\em Noether gauge
symmetry approach} for this $f(R)$ Lagrangian we find out the form of $f(R)$
and the exact solution for cosmic scale factor. It is shown that the resulting
form of $f(R)$ yield a power-law expansion for the scale factor of the
universe.
