Now I know this is one known fact that students just accept. Why is it that anything raised to the power of 0 is 1? We know that , meaning we take the 2 and multiply it three times. So wouldn’t mean we multiply 2 zeroth times, and get back 2? So thats baffling.
This can be solved intuitively, like how we looked at previously. We can look at as the number of ways to arrange a set of number with numbers from to numbers.
Consider . This means we arrange the set of 3 numbers where the numbers are just 1 and 2. So we have
And we find the number of ways to be eight!