Summary: Let \(\tau^{(e)} (n)\) denote the number of exponential divisor of \(n\). Similar to the generalization from \(d(n)\) to \(d_k^{(n)}, \tau^{(e)}(n)\) can be extended to \(\tau k^{(e)}(n)\). It is determined that the function \(\tau_3^{(e)}(n)\) has an asymptotic formula in a short interval.