  The integer $d=\prod_{i=1}^s p_i^{b_i}$ is called an exponential divisor of
$n=\prod_{i=1}^s p_i^{a_i}>1$ if $b_i \mid a_i$ for every $i\in \{1,2,...,s\}$.
Let $\tau^{(e)}(n)$ denote the number of exponential divisors of $n$, where
$\tau^{(e)}(1)=1$ by convention. The aim of the present paper is to establish
an asymptotic formula with remainder term for the $r$-th power of the function
$\tau^{(e)}$, where $r\ge 1$ is an integer. This improves an earlier result of
{\sc M. V. Subbarao} [5].
