Exponential of Product/Proof 2

Theorem

Let $x, y \in \R$ be real numbers.

Let $\exp x$ be the exponential of $x$.


Then:

$\map \exp {x y} = \paren {\exp y}^x$


Proof

\(\ds \paren {\exp y}^x\) \(=\) \(\ds \map \exp {x \map \ln {\exp y} }\) Definition of Power to Real Number
\(\ds \) \(=\) \(\ds \map \exp {x y}\) Exponential of Natural Logarithm

$\blacksquare$

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