in this video we're looking at what powers are if you look at these two expressions here these numbers in the corners are called the powers whereas the three or the a can be called the base so on the left we have the base of three raised to the power of two and on the right we have a base of a to the power of three you might also sometimes see the power being called the order or the index but don't worry about this because power order and index all mean exactly the same thing whatever you call them though all they do is tell you how many times that base needs to be multiplied by itself so 3 to the power of 2 which you could also say as 3 squared just means three times three which is nine so three squared is nine or for a to the power of three which we can call a cubed we could write it as a times a times a it's just that this is a lot longer and messier so we generally keep it in the a cubed form to be able to use powers properly you need to know a whole bunch of rules but in this video we're just going to cover the three most basic ones the first is that anything to the power of zero is just one and it doesn't matter if that's a number like seven to the power of 0 or a variable like p that's to the power of 0. it will always be 1. so 7 to the power of 0 equals 1 and p to the power of 0 equals 1. even if you have something weird like 36 b to the power of zero it's still going to equal one because the whole 36 b is to the power of zero the second rule is that anything to the power of one is just itself so 7 to the power of 1 is just 7 p to the power of 1 is just p and 36 b to the power of 1 would be 36 b this also means that if you had a term like e then you could add a power of one to the corner if you wanted to and it wouldn't have changed its value at all because e is exactly the same thing as e to the power of one the last rule is that if the base of a number is a 1 like 1 to the power of 5 1 to the power of c or 1 to the power of 12 a then the answer will always be 1. so these are all equal to one this is because it doesn't matter how many times you multiply one by itself it's always going to be equal to one for example one to the power of five it's just five sets of one all multiplied together which is still just one anyway that's everything for this video so hope you found it useful if you did then please do tell your friends about us and thanks for watching