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Hello and welcome to this lesson on the law of indices with me, Miss Oreyomi.

For today's lesson you'll be needing your paper and your pen or something you could write on and with.

If you also need to minimise distraction by putting your phone on silence, then please do so.

Or if you need to get into a space with less distraction or less noise, then also please do so.

If you need to pause the video now to do those things, feel free, and then press play to resume the lesson.

Okay, for your try this task you are to work out the exact value for each of the questions you can see on your screen.

So for the first one, you're working on the exact value for this one and for the rest.

What do you notice after you work out the exact value? What is the same and what is different? So take some time now, pause your video attempt all this question and then once you're done, press resume and we'll go for the answers together.

Okay, hopefully you attempted every question.

This would have given you 64, because 2 to the power of 3 is 8, multiplied by 2 to the power of 3 is 8, and 8 times 8 is 64.

This should have also given you 64, 64, 64.

The bottom one should have all, you should have all gotten 8 for the bottom ones.

Now, what is the same about this and what is different? And that is what this lesson is about.

We're going to be learning about the law of indices.

And how why we get answers like this for the first row.

Why all the answers are 64 for the bottom row.

Why all the answers are 8.

Okay, let's look at this first example then.

I've got 2 to the power of 4, which means I'm timesing in 2 by itself four times.

2 times 2 times 2 times 2, and then I'm multiplying that answer by 2 squared meaning I'm timesing 2 by itself twice.

so 2 times 2 times 2 times 2 times 2 times 2.

My final answer is 64.

What of the next one? 3 squared, multiplying 3 by itself twice, and then I'm multiplying 3 by itself three times again.

And that gives me 243, I believe.

Now, let's think about this question.

2 to the power of 4 times 3 squared.

Someone has said this answer is 6 to the power of 6.

Is that correct? Let's work it out.

I've got 2 times 2 times 2 times 2.

And then I'm multiplying that by 3 times 3.

2 times 2 times 2 times 2 is 16.

16 times 9 is 144.

So this gives me 144.

Now if I do Let's choose a different colour pen.

If I do six times : 6 times 6 times 6 times 6 times 6 times 6, I get 46,656.

So we can see, therefore, that 6 to the power of 6 is very different from doing 2 to the power of 4 times 3 squared.

So therefore, is there a generic way I could if I have powers, if I'm multiplying powers together, is there a generic way I could calculate my values? And the generic way is, if I am multiplying powers with the same base, remember, this is our base number here, base here and base here.

Base two and base two is the same.

If I am multiplying powers with the same base, all I have to do is to add the powers.

So therefore, if I am doing this, I'm going to add my powers 4 plus 2 is 6.

2 to the power of 6 is the same as 64.

So over here, 2 to the power of 6 is the same as 64.

Second example, 3 squared times 3 cubed.

Well, 2 plus 3 is 5.

So I could simply have written 3 to the power of 5, and that gives me 243.

Over here, I can't, I have to multiply this out by itself, rather than doing 6 squared because it's not the same base.

I can't simply add the powers.

Okay? So I only add powers when the base number are the same.

Let's try this one then.

I've got 2 squared times 2 squared times 2 squared.

How can I simplify this? Well, I could, because my bases are the same, I could write to the power of 6, which we know is the same as our top one here.

So 2 squared times 2 squared times 2 squared is 64.

So I've got this question now.

I've got 2 squared.

And all of that is raised to my cube.

It's raised to a cube.

So I've got to sweat.

I do what's in my bracket first.

2 squared is 4, and 4 to the power of 3 is 64.

What of this one? 3 squared is 9.

9 to the power of 2 is 81.

Hmm, is there a generic way again, that I could have written that I could have calculated this answer? Well, hopefully you've seen that if the base is the same, when I am multiplying powers in bracket, all I simply have to do is multiply the powers out.

So again, if I change my colour again, go back to red.

For my first one here, I've got 2 squared, all raised to the power of 3.

I could multiply the powers out, which would give me 2 to the power of 6, which I know is 64.

So when you're multiplying powers out, or when you're multiplying powers in brackets, rather, you multiply the powers out.

So what can I write for the second one? I could write 3 to the power of 4.

Which is the same as 81.

How about you try it then? Pause your video, attempt these three questions, and then see how you get on.

Okay, hopefully for this one, you've simply written 5 to the power of 6.

Usually when they tell you to simplify powers, you do not have to write the exact value of what 5 to the power of 6 is raised to unless it's specifically asked.

So when they tell you to simplify the powers, when they have the same base, and you're multiplying, all you have to do is add the powers.

So for the second one, I have 6 to the power of 10.

And for the third one, I've got 8 to the power of 11.

So hopefully you've got those three right.

Let's move on to division then.

Hopefully, you're thinking now if I have to add the powers when I'm multiplying, what would I have to do for this one? Well let's break it down even more.

I've got 5 to the power of 4, so 5 times 5 times 5 times 5, and I'm dividing that answer by 5 times 5.

So 5 times 5 times 5 times 5.

that gives me 625 divided by 25 is 25.

So this here is 25.

What of this one? I've got 6 times 6 times 6 times 6 times 6 divided by 6 times 6 times 6 times 6.

6 to the power of 6 is 46,656 divided by 7,776.

Hopefully, you should your answer is six.

Again, is this correct? A student have said 6 squared divided by 3 squared is 2 to the power of 0.

Let's see if it's correct.

Let's see, that's correct.

So we've got 6 squared, we know is 36 divided by 9.

Well, that is 4, isn't it? And 2 to the power of 0 is not 4.

So we can't do this.

What's the generic rule that we can come up with then if we're dividing powers? Well, we could say that if the base is the same when dividing, then we subtract the powers.

So only if the base is the same, then we subtract the powers, so again let's go over that and just make sure that's correct.

5 to the power of 4 divided by 5 squared.

Well 4 subtract 2 is 2.

So 5 squared is the same of our answer of 25.

Okay? What of this one? 6 to the power of 5 divided by 6 to the power of 4.

Well 5 take away 1.

5 take away 4 rather is 6 to the power of 1, which we know is 6.

Your turn then.

Pause the screen again and attempt this questions.

And then once you once you're done, we'll go over them together again.

Okay, hopefully you had a go at that.

This answer you got to be hopefully you wrote 11 to the power of 5, What of this one? 6,0 which is also the same as 1.

Okay? Now p to the 3, p cubed multiply by p.

If p is here on its own.

What does that mean? If p is here on its own, it means it's raised to the power of 1, right? So this is going to be p to the power of 4 divided by p squared, which we know is the same as p squared.

Right.

We are now going to move on to your independent task.

You are to pause your screen, attempt every single question, and then resume your video and we'll go over the answers.

So pause your screen now and attempt every question on your independent task and then resume the video for us to go over it.

Okay, let's go over the answers then.

So we've got t to the power of 5 multiplied by t to the power of 3.

Well, we're adding the powers aren't we? So it's going to be t to the power of 8.

7 to the power of 4 divided by 7 to the power of something, we know that something here is 1, so it's going to be 7 to the power of 3.

Next one, 6 8 times 6 to that's 6 10, divided by 6 to the power of 5.

So our final answer is 6 raised to the power of 5.

Over here we're subtracting because we're dividing, so it's going to be a raise to the power of 3, a cubed.

Over here we've got three numbers, 3 plus 1 plus 5, that is 8 to the power of 9.

Okay.

Over here we've got 4, adding and subtracting 5, because it's the powers we're doing 4 adding negative 5.

So hopefully your answer is 3 to the negative 1 raised to the power of minus 1.

Next ones then.

Want to match this expression.

Well, 4 to the power of 4 times 4 squared, hopefully you match, you matched a 2 to 5, Hopefully you matched b to 3.

4 to the power of 5.

So this would be 4 to the 7 divided by 4 to the 11.

Or it's going to give us a negative number, isn't it? So it's going to be that one there.

This one is going to be that which leaves e which is 4, because we're multiplying the powers out.

For your explore task.

This is quite interesting actually.

Can you put the numbers 0 to 9 in places in these boxes to make three statement true.

So for example, if you use 2 and if you use 1 here, this would be 3.

So you need to use numbers 0,4,5,6,7,8 in other places in this box to make three true statements.

So attempt this now.

How many different ways can you do this so that the numbers 0 to 9 are filled in the empty boxes on your screen.

Pause the video now and attempt this.

And when you come back, I would go through an example with you.

So pause the video now to attempt your explore task.

Okay, so this is an answer that I came up with.

I've got 0 here, I've got 2 here 3,4,5,6,7,8,9 on one as well.

So for example, x 4 x raised to the power of four, or brackets raised to the power of 5.

That gives me x to the 20 x to the power of 8 divided by x to the power of 7 gives me x 1 and x to the power of 3 multiply by x to the power of six.

That gives x to the power of 9.

Which ones did you come up with? Did you find many ways of doing this? Or did you just do it in one way? Okay, a very big word on to you for completing today's task and attempting every single question.

I hope you found it interesting.

I hope you learned something new.

And I hope before you go you complete your quiz, just to show yourself what you learned from today's lesson and also to prepare yourself for the next lesson.

And I will see you at the next lesson.

Bye.