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Hi, my name's Charles and I'm one of the Math teachers from the Maxim Workshop. I'm just going to now teach you how to do some math. I'm going to show you how to multiply exponents. Now, an exponent is basically the numbers that you find as the superscript to another number. So, we might have something like this: "a" is the power of 5. So this is the power, more commonly known as the indecie. Now, if you want to know what to look at what this actually means in full, you would say you have an "a" being multiplied by itself and you need to write out that many a's. So five a's. So we've got one, two, three, four, five a's multiplied together and that is pretty much the definition of this. So, what happens when we try to multiply "a5" by say, another number? The first thing we need to know is that we can only multiply the exponent by another exponent directly when the bases are the same. So the powers can be different, but the base which is "a", has to be the same. So, what I'm basically saying is if we have "a5", we can only multiply directly by "a" with another power. So, we'll take "a2". Now, when we multiply an exponent like this, you need to remember that you add the tops, so you add the powers. So "a2 x a5" is basically "a7". Now, if you don't want to take my word for that, what we can do, we can actually establish that from this definition. So, if we look at what "a2" is, that's pretty much "a x a". So, if this "a5" equates to this and this "a2" equates to this, we can multiply this by that to prove we have "a7". So, "a^5" is pretty much this, "a x a x a x a x a" multiplied by "a2", which is this, "a x a". Now, what we would need to do is count up how many a's we have to establish what power we're going to have when we multiply these two things together. So, we've got "a1 x a" that's "a2", times "3 to the 4 to the 5 to the 6 to the 7". So that gives us "a7", and that's proof that "a5" when multiplied by "a2" equals "a7", and that's how to multiply exponents. .
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