Why is the base of an exponential function limited to the set of real numbers greater than zero?

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From Rogawski, Jon (2011-04-01). Single Variable Calculus (Page 339). W. H. Freeman.

An exponential function is a function of the form $f (x) = b^x$, where $b > 0$ and $b \neq 1$.

Why is $b$ limited to the set of real numbers greater than zero?