In this paper, a method based on the Lempel-Ziv -Welch compression encoding scheme is proposed for evaluating cascade exponentiation. 
. The Lempel-Ziv-Welch compression algorithm has the effect of dynamically increasing the window size of Yen and Laih's method [11]. Some experiments have been carried out to compare the performance of the proposed method with those of previous methods. From the experimental results, we find that our approach is indeed feasible, and that the merits of our method become more pronounced for large bi's.