  Let $\cal R$ be either the Grothendieck semiring (semiring with
multiplication) of complex algebraic varieties, or the Grothendieck ring of
these varieties, or the Grothendieck ring localized by the class of the complex
affine line. We introduce a construction which defines operations of taking
powers of series over these (semi)rings. This means that, for a power series
$A(t)=1+\sum\limits_{i=1}^\infty A_i t^i$ with the coefficients $A_i$ from
$\cal R$ and for $M\in {\cal R}$, there is defined a series $(A(t))^M$ (with
coefficients from $\cal R$ as well) so that all the usual properties of the
exponential function hold.We also express in these terms the generating
function of the Hilbert scheme of points (0-dimensional subschemes) on a
surface.
