Product Notation: Expressing Prod_{n=1}^k a_i

[1+1=1]

I have a quick question. In my book, there is a question that says to express each of the following products in terms of $$\prod_{n=1}^\k\a{i}$$, where $$k$$ is constant. Now, my question is this: $$\prod_{n=1}^\k\$$ka_i. Would i just pull the $$k$$ out because it is only a constant and move that to in front of the product? This almost looks like a property that is similar with summation, but I think I have to do more than simply move the $$k$$. Anyone understand/assist? Thank you all. I hope everyone can understand my LaTeX. The number atop the product is supposed to be k, NOT 1. Damn latex.

 

[sic]

no, you multiply by k every time, meaning that outside it would turn into k^k

 

[1+1=1]

Ok, so on the outside of the product, I would have k^k=product a_i?

I have another question that just blows my mind:

The product is the same, but it reads ia_i. There is no k in the question, how am I to write this in terms of k??