The Maths Prof: The Rules of Indices / Exponents (part 1)

[music], hey guys, i’m the mascot and today i’m going to show you the rules of indices? So these are just the power rules that you need to remember so before i get started? I just want to point things out. These are the basic rules that you need whenever at your time, see two letters together. They are the same two numbers together, but on the same you’re allowed to as the powers together whenever you’re dividing two letters that the same you subtract the powers and finally, if you see bracket, then you multiply the powers?

So let’s have a look at the first one. So i’ve got two letters that are the same, so the powers will supply and because we’re multiplying them together.

We need to remember to as the powers so in the first one i’m just doing two subtrees, which is five okay on to the next one! So before i do this one i just want to point out this x here there isn’t a power on the egg. It’s up to you to remember, there’s like an invisible one here that we don’t normally write. So now we can subtract because remember when we did writing you have to subtract the powers so i write my x value down and six take away. One is five. Okay, so you’ve got the same answer now on to the next one. This time we’ve got bracket. Whenever you see brackets, it means you must multiply the powers together.

So in this one, two multiplied by 7 is 14? Now the fourth one is another wall, something else you need to remember. Whenever you see a letter or number with the power of 0, the answer is just one: no matter what semester or what number you have.

If you see the power of zero is always equal to the number one? My answer bottom one so here i’ve got to try for well. We know how to multiply numbers so 2 times. 4 is just 8, so you just multiply the numbers abnormal? Then now we’re going to look at the powers. So remember that if you don’t see a power, there’s like an invisible one here and also remember the 1, the power rules only apply when the message is the same. So first i’m going to look at the x value so remember from multiplying or adding the powers together so for the x’s we’ve got 1 plus 3, which is 4, and now i’m going to look at the y value!

So again, it’s multiplied so we’re adding the powers together and the y letters, so 2 plus negative 6 is negative 4 and we can’t do anything else with it. We can’t find these letters together, okay, because the power rules only work with the letter is the same, and these letters are different? Okay, now i’m going to make them a bit harder! Okay, so is this top one up here? i’m dividing! remember if you just see normal numbers, you just divide them as normal. So 36 divided by 4, is just equal to the number 9 and now i’m going to look at the letters individually to work out what happens for the powers.

So first i’m going to look at the end value. So then write down n and remember 4 divides! you have to subtract the powers so for the m, we’ve got three take away, 7, which is negative, 4 and now i’m, going to look at the end value so again, i’m subtracting the powers, so i’ve got minus to take away negative 10, so be careful there, because you’ve got a double -, you’re doing – to take away, and then this happens to be negative. Remember when you see two negatives together like this, they turn into a plus, so negative, 2 plus 10 is equal to 8! So that gives me the power on the end so that one’s done now this one here, a lot of people make respect from this one because they see the bracket and i think i’m going to multiply the power?

But then they forget about this number here. Remember this square effect everything inside the bracket! So you have to square this number two as well, so this too don’t forget?

This has like an invisible power of one okay that we wouldn’t normally write, but you need to remember that it’s still there, so you have to multiply every single power inside the bracket by two.

So that would give me 1 times.

2 is just a 2, so the x values you’ve got 6 times 2, which is 12, so the y values we’ve got minus 2 times 2, which is minus 4 and lastly, to the z 1 times 2, which is 2. Now that’s correct, but becomes simplified it’s a little bit? It could 2 squared because 2 squared 2 times 2, which is 4 so i’m, just going to write.

My final version like that, ok, so just like in the previous previous example? Remember. This power affects everything inside the brackets, so even that number 3 at the beginning so remember to multiply all the powers here by 3!

So it’s 1 1 times 3 is just 3 for the n values. We’ve got 4 times 3, which is 12 and lastly, n 6 times 3, which is 18 and again just evaluate that yaxley q3s cube is 3 times 3 times 3, which is 27, and everything else stays the same. Remember you can’t do anything else with these letters pina, because they’re different letters, so the rules, the powerwall, don’t apply when you have different letters. So that’s finished now on to this one. Yet so this one is actually just like the one at the top here, it’s divided remember when you see a fraction that just means divided to reduce the numerator divided by the denominator, so we’re going to look at the numbers first for we’ve got 21 divided by 3, which we can work out. It’s just seven and now i’m going to look at the vector. A so remember, there’s like the invisible one on these letters that don’t have powers so for the a well one take away. One is just zero for the b values! We’ve got four cakery 1, which is 3 and for the city we’ve got 7, take away negative 3 or chance. The double miners, so several clocks meet, which is 10 but i, can do something else with this one remember earlier, i told you that any letter or any number that has a power of 0, is equal to the number one well i can season it. I’ve got a to the power of 0, which is equal to 1! Well, these will be multiplied together. So if this is one certainly times, 1 is just 7, so i can just type it up a little bit and write it like that? So that makes sense, because if i’m is over here when i’m dividing, we could have actually just cross those out straight away, because whenever you divide something by itself that a to the 1/8 to the 1 well, they just cancel each other out, because how many a one is anyone just one? ok, so you could have crossed them out there or, if you forget to do that- and you see this idea just remember anything to the power of 0 is equal to 1? Okay, i put one more challenge question to finish all right? So in this last example, it’s not really about it’s more difficult.

It’s just a longer question and lots of working out i’m, not showing you any new rules, so in this first one just before i get started so i don’t forget to do it later on i’m going to just add the powers of one to all of those methods that don’t have powers?

Okay and now i’m going to get started so i’m going to work on out what happens to the numerator. To start with, remember when you’re multiplying, you must add all the powers together. So, firstly, the numbers 4 & 6, well, i’m, just multiplying those numbers as level so 4 times. 6 is 24.

Now i’m going to go to the x-values and i’m going to add their powers together so for the x value is but 1 plus 1, which is 2. Okay. Now for the y value, we’ve got 1 plus negative 6, which is negative 5 and finally, the series values and we’ve got 3 plus 10, which is 30! Okay, stop editing the powers to get up now. This denominator is still there. It hasn’t changed just yet and remember when you see a fashion like this, it means we’re dividing so we’re subtracting two powers.

So the numbers just as before you just divide those normal, so 24, divided by 8, is just 3. Now i’m going to look at the x value, so i’m subtracting and then to take away 1, which is just 1 now for the y values. I’ve got minus 5 minus minus 2, which is the same as minus 5, plus 2, which is minus 3 and lastly, for the p value 13 take away 5, which is just 8 okay, so for this x value here, i’d be right to the power of 1. But remember you don’t have to write that? okay, you can just leave it like that. So they’re, the basic rules of indices, the power rules, have another video with other rules, hard questions, but that’s more for the extended little bit, so it may not be in your end exam?

So anyway, that’s all from me for today and goodbye [music]. ?