(related to Proposition: Exponential Function of General Base With Integer Exponents)
It has been shown already, that for positive real numbers a > 0 and an integer n\ge 0, the n-th-power function equals the exponential function of general base with natural exponents: a^n=\exp_a(n).\quad\quad( * ) Let n < 0. From the reciprocity law, it follows a^{-n}=\frac{1}{a^n}=\frac{1}{\exp_a(n)}=\exp_a(-n). Thus, ( * ) is valid for all integers n\in\mathbb Z.
