We propose a generic negative correlation between power-law scaling and Hurst exponents for size/magnitude data from real and synthetic earthquakes. The synthetic earthquakes were produced from a conceptual earthquake model, the long-range connective sandpile (LRCS) model. The LRCS model is a new modification of sandpile models that considers the random distant connection between two separated cells instead of neighboring cells. We calculated the Hurst exponent H and the power-law scaling exponent B for event size data in the LRCS model. We systematically explored the relationships between these two exponents (H and B) and conclusively obtained a negative correlation between H and B. We also found this negative correlation for real earthquake data registered in the Taiwan Central Weather Bureau (CWB) catalog. This negative correlation has not been demonstrated previously for real seismicity, although it has been frequently suggested.