Q:

How would I solve $φ(2^{100} · 3^{20} · 19^{200})$?

I don't even know how to begin this question because solving the numbers inside the parenthesis is too high to be solved. $φ$ is Euler's Phi Function.

A:

$\varphi(2^{100}3^{20}19^{200})=2^{99}(3^{20}-3^{19})(19^{200}-19^{199})$.  
Here I used that $\varphi(p^n)=p^n-p^{n-1}$ and that $\varphi$ is multiplicative.

