Earthquake cumulative frequency-magnitude (CFM) distributions are described by the Gutenberg-Richter power law where the exponent is the b-value. Although it has been reported that the b-value changes before large earthquakes, we find that an upper-truncated power law applied to earthquake CFM distributions yields a time-independent scaling parameter, herein called the α-value. We analyze earthquakes associated with subduction of the Nazca plate beneath South America and find a region of isolated seismic activity at depths greater than 500 km between 20° S and 30° S. For the entire record, 1973-2000, the earthquake CFM distribution in this isolated region is well described by a Gutenberg-Richter power law with b = 0.58. The data set includes several large seismic events with mb ≥6.8. A power law applied to the CFM distributions for short time intervals between the large events yields b-values greater than the b-value for the entire record. CFM distributions for the short time intervals are better described by an upper-truncated power law than by a power law. The α-value determined by applying an upper-truncated power law to the short time intervals is equal to the b-value obtained by applying the Gutenberg-Richter power law to the entire record. Temporal changes in b-value are due to temporal fluctuations in maximum magnitude. Analysis of four Flinn-Engdahl regions, two in subduction zones and two along spreading ridges, demonstrates wider applicability of the results. The α-value is an unchanging characteristic of the system that may be determined from a short-term record.