  We study the inverse problem of determining the coefficients of the
fractional power of a general second order elliptic operator given in the
exterior of an open subset of the Euclidean space. We show the problem can be
reduced into determining the coefficients from the boundary Cauchy data of the
elliptic operator on the open set, the Calder\'{o}n problem. As a corollary we
establish several new results for nonlocal inverse problems by using the
corresponding results for the local inverse problems. In particular the
isotropic nonlocal Calder\'{o}n problem can be resolved completely, assuming
some regularity assumptions on the coefficients, and the anisotropic
Calder\'{o}n problem modulo an isometry which is the identity at the boundary
for real-analytic anisotropic conductivities in dimension greater than two and
bounded and measurable anisotropic conductivities in two dimensions.
