We prove the exponential law A(E × F,G) ∼= A(E,A(F,G)) (bornological isomorphism) for the following classes A of test functions: B (globally bounded derivatives), W∞,p (globally p-integrable derivatives), S (Schwartz space), B[M ] (globally Denjoy–Carleman), W [M ],p (Sobolev– Denjoy–Carleman), and S [M ] [L] (Gelfand–Shilov). Here E,F,G are convenient vector spaces (finite dimensional in the c...