At least one probability

At least one and none are complements, so $P(\text{at least one}) = 1 - P(\text{none})$ and you only ever compute one product. Roll a fair six-sided die 4 times: the chance of no 6 on a single roll is $5/6$, and because the rolls are independent the chance of no 6 on all four is $(5/6)^4 = 625/1296 \approx 0.4823$. So the probability of at least one 6 is $1 - 0.4823 = 0.5177$. The power step needs the trials to be independent with the same success probability on each one.