# Lesson video

In progress...

Hello.

I'm Mr. Linton and today we're going to be looking at indices in index form.

All you're going to need is something to write with and something to write on.

Try to make sure you're in a quiet space with no distractions.

How many dots are in each of the images below? Describe how the sequence could grow.

Pause the video and make some notes.

When you're ready unpause it and we'll go through it together.

You can pause in three, two, one.

Okay.

Let's have a look.

The first one consists of three dots.

The second one is three lots of three dots.

Well, you might say it's three times three.

Which is nine.

Now the next one, if you look really closely, that bit there is what we have here, isn't it? We have three lots of them.

So we've now got three lots of the three lots of three dots.

Which is three multiplied by three, multiply by three.

Which is 27.

We look at this next one, that section there is all of that there, and we've got three of them.

So we've actually got three lots of three lots of three lots of three lots of dots.

That's a little bit of a weird thing to say, isn't it ? We're going to use these lessons today to look at some easier ways to write that down.

We can use index notation to describe these repeated products.

And repeated products, is where we're multiplying the same number again and again and again.

So in the first one, we've got one lot of three dots.

It's three to the power of one, which is just three.

In the second one, we've got three lots of three dots.

So three multiplied by three or three squared.

It's two threes' multiplied together.

In the next one, we've got three lots of three lots of three dots.

Which is three multiplied by three, multiply by three.

Okay.

Right now, there's three cube three to the power of three Set full form.

What would that look like? Would that look like three to the power of four? Cause we're multiplying three, four times.

Sorry that should be an equal sign.

Three, multiply by three, multiply by three, multiply by three.

Or three lots of three lots of three lots of three dots.

Sorry, different question now.

What if we had four lots of four lots of four dots.

So in that case, we've got four lots, of four lots, of four dots.

And that's going to be, four to the power of three like that.

Okay.

Now you have plenty of time to go to go.

Pause the video and access the worksheet.

When you're ready, you unpause it.

We'll go through the answers together.

If you want some hints, just keep the video playing just a little bit and I'll go through the first few and I'll go through the rest of the afterwards.

Good luck.

How did you get on? If you want some hints first, I'm going to go through one part of each question with you now.

I'll do part b.

Whereby six multiplied by six, multiply by six, multiply by six multiply by six.

So six, this six is being multiplied together five times.

That's not the same as six multiplied by five or six to the power of five.

Question two.

You need true or false one.

Let's go for, let's go to C.

Eight to the power of three.

That's going to to be false.

It's not the same as eight times three.

Eight to the power of three means eight times eight times eight.

Question three.

Place the correct symbol between the science.

Let's have a look at C.

So three cubed, is three multiplied by three multiply by three, 27.

Five squared is going to be, five multiply by five which is 25.

Now 27 is the greater than 25 so I'm going to need this symbol here.

Like that.

And finally not sure what the calculations.

These were a little bit different to everything else we've done.

Because it's the first time I've introduced two different numbers in the same product.

So I'll do A.

Two multiply by two, multiply by seven, multiply by seven, multiply by seven.

So two multiply by two is two squared, seven times, seven times is seven cubed.

So it's going to be this answer here.

Now if you've noticed we've not done two times seven to get 14.

We kept, we said how many twos' we multiplied and how many sevens are being multiplied.

So those two and that you want it like that.

Now, if you want to carry on, pause it again, have a go.

I want to go through the rest of the rest of the answer in a moment.

If you want to pause, do it now.

Three, two, one go.

Okay.

Time for the rest of the answers.

Six eight will be six squared.

Sorry.

One A is six squared.

And one C, is going to be two to the power of five.

Part D.

Find the product of parts A and B.

So A, was six squared and B was six to the power of five.

So how many sixes' am I multiplying together? One times two to three, four, five, six.

There are seven of them.

They multiplied together.

So six to the power of seven.

True or false nine to the power of one is equal to nine.

That's true.

Five cubes can be written as 25 times five because 25 is five times five, Isn't it.

By another five, I've got five cubes.

So that's true.

Eight to the power of four, eight times, eight times, eight times eight.

That's true.

And five cubed is three times, three times, three times, three times three.

So that's three multiplied by itself five times.

That's false.

Five cubed would be five times, five times five.

Now these threes here are multiplied together.

That's three in multiplied.

We've got, we've got five of those three's multiplied together on weight.

So that's three to the power of five is what that is.

That's not the same as five to the power of three.

Question three.

Two cubed would be eight and three squared is nine.

So 8 smaller than nine, Isn't that.

Right? Three B.

This is one of my favourite ones.

It's two to the power of four is two times two, which is four times two which is eight times two is 16.

And four squared is 16 and four times four is 16 in test.

That's very equal.

You wouldn't necessarily think to look at first, but can you see that this first one, two to the power four, is going to be two times two multiply by two times two.

Which is the same as four times four isn't it? And question D.

They're also equal because once the power of 8 is one times, one times, one times, one times, one times, one times, one times one.

Which is one.

I'm not right so I want the power to find it as well, because I'm sure that you understand that's also one.

Let's go on to question four.

Note the calculation on the left.

So in this case, I'm multiplying two fives' and multiplying two threes'.

So I'm going to have three squared and a five squared.

That's there.

C I've got three of these fives multiplied together so that's applied to the power of three.

I've got one, three.

Three multiplied by five to the power of three.

And here I've got two squared and seven squared multiplied together.

And of course that's going to be that one.

We'll finish with the explore activity.

An array has to be made out of copies of this five by five by five cube.

How many ways can you express the total number of small cubes? Close the video and have it go.

When you're ready on unpause it and we can go through it together.

You can pause in three, two, one.

Okay.

Let's have a look.

There are lots of ways that we can look at this.

One of those cubes is five by five by five.

Isn't it? And how many of these cubes we got? Altogether we've got 25 of those cubes.

So you could say we've got 25 lots.

By five by five by five.

You could say, that actually we've got five lots down the side, multiplied by five lots there.

And each cube, is five by five by five.

You could say that we've got a square made up of five by five.

So five squared and each cube, is five cubed.

Five by five by five.

You could say that we've got well, if we multiply five of those times like that together, then it's five to the power of five.

Just a few ways that you could write it.

You might come up with some of your own.

Just one more.

Just quickly in that five by five by five cube.

How many small cubes are there altogether? Five times five is 25 multiply by five to 25, 50, 75, 100, 125.

So we've got 25 cubes made up.

We have two of cubes having 125 small cubes in it.

There's another one as well.

Right? I'll leave it there for now.

That's the end of the lesson.

I'll see you later.

Goodbye.