Express the product of a binomial distribution for i = 1 to n as a sum

Question

I am told that $$f(y|p) = \prod_{i=1}^n (1-p)^yp $$ $$=p^n(1-p)^{\sum_{i=1}^n y_i}$$ What are the steps to get there?

Answer 1

Steps:

$$\begin{split}f(y|p)&=\prod_{i=1}^n(1-p)^{y_i}p\\ &=\underbrace{p*p*...*p}_{\text {n}}*(1-p)^{y_1}*(1-p)^{y_2}*...*(1-p)^{y_n}\\ &=p^n(1-p)^{y_1+y_2+...+y_n}\\ &=p^n(1-p)^{\sum_{i=1}^ny_i}\end{split}$$