Different approaches for solving power functions in Java were discussed, highlighting the importance of performance optimization.Recursive approach had time complexity of O(n) and space complexity of O(n) due to call stack, leading to performance issues for large values of n.Binary exponentiation reduced time complexity to O(log n) by leveraging mathematical insights, providing significant performance improvements.Fast exponentiation algorithm was recommended for optimal performance, especially for handling large exponents, with a comparison provided for 2^1000.