This work proposes an exponential computation with low-computational complexity and applies this technique to the expectation-maximization (EM) algorithm for Gaussian mixture model (GMM). For certain machine-learning techniques, such as the EM algorithm for the GMM, fast and low-cost implementations are preferred over high precision ones. Since the exponential function is frequently used in machine-learning algorithms, this work proposes reducing computational complexity by transforming the function into powers of two and introducing a look-up table. Moreover, to improve efficiency the look-up table is scaled. To verify the validity of the proposed technique, this work obtains simulation results for the EM algorithm used for parameter estimation and evaluates the performances of the results in terms of the mean absolute error and computational time. This work compares our proposed method against the Taylor expansion and the exp() function in a standard C library, and shows that the computational time of the EM algorithm is reduced while maintaining comparable precision in the estimation results.