Pi Product Simplification Rules

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I wanted to know the "rules" for Infinite Products. For example, if you have a factorial, what do you do? A power? A power with two variables?

What are some quick things I can look at and immediately know the simplification of, basically?

Edit: here is an example:

$\lambda * e^{-\lambda * y_i}$

I have to find this infinite product from i=1 to inf.. how? I dont want to know how to do just this problem. I want to be able to do it for all.