  The different between the inverse power function and the negative exponential
function is significant. The former suggests a complex distribution, while the
latter indicates a simple distribution. However, the association of the
power-law distribution with the exponential distribution has been seldom
researched. Using mathematical derivation and numerical experiments, I reveal
that a power-law distribution can be created through averaging an exponential
distribution. For the distributions defined in a 1-dimension space, the scaling
exponent is 1; while for those defined in a 2-dimension space, the scaling
exponent is 2. The findings of this study are as follows. First, the
exponential distributions suggest a hidden scaling, but the scaling exponents
suggest a Euclidean dimension. Second, special power-law distributions can be
derived from exponential distributions, but they differ from the typical
power-law distribution. Third, it is the real power-law distribution that can
be related with fractal dimension. This study discloses the inherent
relationship between simplicity and complexity. In practice, maybe the result
presented in this paper can be employed to distinguish the real power laws from
spurious power laws (e.g., the fake Zipf distribution).
