hello welcome back to the physics course here we're going to continue reviewing essential core concepts in algebra to help us do well in physics in this last review of the core parts of algebra we're going to talk about exponents we're going to talk about solving simple equations and I'm going to review quick graphing with you just to make sure we're on the same page with all of these skills same thing as last time if you watch this lesson and you're scratching your head and you're thinking I don't get that that makes no sense at all then it doesn't mean that you're not smart it just means that you need to review some algebra skills so this is a review but if it doesn't make sense go back to my algebra course and work through the first part of that where we start solving equations and graphing because I have I blow it up into many many many examples there so the first thing we're going to do is just quickly review exponents it's we use them all the time in physics you will find out that we use them in our problems and we also use them in our units like Killough kilometres centimeters they all involve exponents so we're gonna use exponents all the time so to refresh your memory the exponent or the number three raised to the exponent two three to the power of two what it means mathematically is we take that bottom number three we multiply it by itself two times this does not mean three times two it means three times three you're multiplying this times itself as many times as is specified in the exponent so as you know three times three is nine so that's what the answer is just three squared it's nine now what if you had the number two raised to the power of three well what that means is you take the bottom number multiply it by itself how many times well you do it as many times as the exponent says so 2 times 2 is 4 4 times 2 is 8 so 2 to the power of 3 equals 8 now the rest of these examples I'm all gonna you know the concept of an exponent can apply to any number I can take 147 and I can raise it to the power of 4 like 147 to the power 4 that would be 147 times 147 times 147 times 147 I've done it four times because I took 147 I raised to the power 4 but in reality you don't do that too much in physics we use exponents for some things but usually you're not doing that kind of thing too much with large numbers but we do use powers of 10 all the time so exponents can be applied to any number we can do there were anything but we have a special relationship with the power of powers of 10 and you'll see why as we get a little farther in the class but if I take the number 10 and I raise it to the power of 1 what does that mean well that means I take the bottom number and I multiply it by itself well it's a little bit confusing I say multiplied by itself you think I'm gonna multiply again by 10 but what I'm trying to say is look at the pattern here we we wrote down two threes and multiplied them here we wrote down three twos and multiplied them but here there's only one so really it's just ten we don't won't write anything else down because it's already there one time so 10 to the power of 1 is 10 10 to the power of 2 that's gonna be 10 times itself so 10 times 10 that's gonna be 100 right 10 to the power of 3 you're gonna see these types of exponents all the time it is what take the bottom number 10 times itself times itself again 3 times again because of the exponent 10 times 10 is 100 times 10 again makes it 1,000 1,000 now these are larger and larger powers so as I get higher and higher notice what's happening I went from 10 to a hundred to a thousand so every time I increase the exponent I increased times 10 every time that makes sense because I'm in multiplying by 10 each time I go down the list but here's the thing that blows your mind or blows a lot of people's minds you can actually have exponents without that aren't positive numbers here they're actually negative numbers here all right so if I have 10 to the power of negative 1 what do you think that means well first you're like well how can I multiply 10 times