A power law is a functional relationship between two quantities where one quantity varies as a power of another. This relationship is often represented in the form $$y = kx^a$$, where $$k$$ is a constant, $$x$$ is the independent variable, and $$a$$ is the exponent that determines the nature of the relationship. Power laws are significant in various fields, including fractal geometry, as they reveal the underlying patterns and structures in complex systems, highlighting how certain phenomena can exhibit self-similarity and scale invariance.
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