TITLE: Xmas Maths 2017: The value of a $\color{red}m^{\color{green}{ince}\ \color{orange}{\pi}}$ and $\color{red}\pi^{\color{green}{ie}}$
QUESTION [8 upvotes]: In the spirit of the festive season!
(i) Evaluate 

$$\large \color{red}m^{\color{green}i\color{orange}n\color{red}c\color{green}e\;\color{red}\pi}$$

given that 
$m=12\;\;\text{(month when mince pies are consumed)}\\
n=5\;\;\text{(number of points of the star on a mince pie)}\\
c=2.997\times 10^{8}s^{-1}\; \text{(rate at which mince pies are consumed!)}\\
$
(ii) It is well known that $e^{i\pi}=-1$, but what is the value of 

$$\large\color{red}\pi^{\color{green}{ie}}$$

?
Merry Christmas!

REPLY [3 votes]: $$\color{blue}{\text{ii}}$$

$$\large\color{red}\pi^{\color{green}{ie}}=\left(\color{green}e^{\ln(\color{red}\pi)}\right)^{\color{green}{ie}}=\left(\color{green}e^{\color{green}{i}\color{red}{\pi}}\right)^{\frac{\color{green}{e\color{black}{\ln(}\color{red}\pi\color{black})}}{\color{red}\pi}}=\big(-1\big)^{\frac{\color{green}{e\color{black}{\ln(}\color{red}\pi\color{black})}}{\color{red}\pi}}.$$