A power-law series is a mathematical sequence where each term is a multiple of the previous term, raised to a fixed power. This type of sequence is commonly used in physics, economics, and other areas of research where patterns need to be observed and analyzed. Synonyms for power-law series include power series, geometric sequence, and exponential sequence. Some researchers may also refer to it as a fractal sequence, due to the infinitely repeating pattern that it creates. Ultimately, understanding the terminology and nuances of a power-law series is critical to drawing accurate conclusions and making informed decisions based on its behavior.