I'm trying to understand why when simplifying the exponential likelihood function, the symbol changed from a product of sequences to summation and why isn't the theta in the exponential to the power of n?.
$$ \ p(y | \theta) = \prod_{i=1}^{n} (\theta \cdot exp(-\theta \cdot y_{i}) $$
$$ \ p(y | \theta) = \theta ^ {n} \cdot \prod_{i=1}^{n} exp(-\theta \cdot y_{i}) $$
$$ \ p(y | \theta) = \theta ^ {n} \cdot exp(-\theta \cdot \sum_{i=1}^{n} y_{i}) $$