Exponential of Product/Proof 1

Proof
Let $Y = \exp y$.

From Exponential of Natural Logarithm:
 * $\map \ln {\exp y} = y$

From Logarithms of Powers, we have:
 * $\ln Y^x = x \ln Y = x \, \map \ln {\exp y} = x y$

Thus:
 * $\map \exp {x y} = \map \exp {\ln Y^x} = Y^x = \paren {\exp y}^x$