Lesson video

Hello, and welcome to this lesson on fractional indices part one, with me, Miss Oreyomi.

For today's lesson, you will be needing a paper and a pen or something you could write on and with.

So if you need to pause the video now to go get those, then please do so.

Also, if you can minimise distraction by putting your phone on silent, and also trying to get into a space with less noise, that would really help you to concentrate.

So again, if you need to do that, please do so now and then resume the video when you are ready to begin the lesson.

Okay.

Let's look at how you try this task.

Copy and complete each question.

You must use the same number to fill in every box for question.

So let's take a look at question one.

So this is just an example before you have a chance to go ahead and work it out yourself.

I must use the same number to fill every box per question.

So for the first one, I've used two to the power four times two to the power four remembering that I add the powers when I'm multiplying numbers with the same base.

Indices with the same base rather.

So, pause the screen now.

Attempt every single one, and then press resume to, for us to go over the answers together.

Okay.

So the first one has been done for you.

Two to the power of four times two to the power of four gives you eight.

Let's move on to this two to the power of nine.

Well, hopefully you've written three, three, and three.

For this one hopefully you did, three and three.

Because three plus three is six.

This two and two, because two times two to the power of two times two to the power of two is two to the power of four.

Here will be two to the power of one and two to the power of one.

Here two to the power of two, two to squared times two squared times two squared.

Here is two to the power of one, one and one.

Okay.

Here.

Did you get, a third, a third and a third? And for this one, did you get a half and a half? Because, one third plus one third plus one third gives you one.

And a half plus a half gives you one.

This, try this task, especially these two is what we're looking at in today's lesson.

So let's get on with it.

Let's go back to the example we just went through.

We've got one third plus one third plus one third.

This here is known as fractional, indices.

Remembering that previously we did two to the power of three and we said this is a power, right? Well, our power here was an integer.

Wasn't it? Whereas in this case, our power is a fraction.

Hence, the name fractional indices.

And then for here I've got one over two and one over two, just to recap from our try this task.

So in general, when I have a fractional indices, when I have a fractional indices and I've got it two to the power n, n being any number, any integer.

This is the same as writing the root of n.

So n being my denominator raised to the base I was given.

This will make sense with some examples.

So ,take the first one, a to the power of a half.

This is the same as saying a, a being my base, raised to the square root because two is the same as a square root.

So for example, if I've got nine raised to the half, this is the same as writing nine my base, to the square root of.

So finding the square root of nine.

Because this symbol is a square root, I don't have to write the two.

Okay? But this would be three.

So therefore nine raised to the half is three.

Let's do another example.

If I say 25, raised to the half.

I am going to write the root, the square root of 25.

Again, because this already means square root.

And this two, this two here mean take the square root of nine.

I don't have to write the two there again.

So I am just going to write five.

What if our number is raised to a third? Well, my denominator goes outside of my root symbol and I'm raised and I'm inside my root and I've got my base number over here.

So let's try another example.

Let's say 27 raised to a third, 27 raised to a third.

Well, my three, my denominator is going to go outside of my root symbol and my base number 27 is going to go inside my root symbol.

So essentially 27 raised to a third is asking me to find the cube root of 27.

What number can I times three times that would give me 27? By itself three times It'll give me 27? It's three.

Isn't it? Because three times three times three is 27.

So, my answer is going to be three.

Therefore, 27 raised to a third, is the same as finding the cube root of 27 and my answer is three.

Let's do another one.

Let's do 64? 64 and a third.

What number, check that, can I times, by itself three times that would give me 64.

So I could write this as three, cube root of 64, four times four times four is 64.

So my answer here is going to be four.

What if, we've got the fourth root of a number? So here, my denominator is four.

So that four is going to go outside of my root symbol.

So take for example, I've got the number 16.

Okay.

And I'm going to put the four there and I'm going to find the fourth root of the 16.

Well, that is two.

Isn't it? I'm just going to write this again.

So first I start with 16 raised to a quarter.

I am going to put my four outside of my root symbol, put my 16 inside, and that's going to give me two.

Because two times, two times, two times two is 16.

Why don't you have a go at that? I want you to write this.

Write the root symbol first, and then simplify your answers.

So something like this, and then your answer for the three of those.

So pause your screen now, try these three questions and then press resume or we can go over it together.

Okay.

Hopefully you had a go at these.

So we've got out of written 81 here, cause it's asking me for the square root of 81.

My answer is nine.

This one again is asking me for the square root of 144.

That is 12.

Last one is asking me for the cube root of a 1000.

That is 10.

So, say for example I have been given this number like so, and someone tells me to write this in index form.

How could I do that? Well, if the question is right in index form.

Index form means I need a base raised to a power.

What's going to be my base? It's going to be 125.

Isn't it? What does this symbol mean? It means the root.

And the three here means? A third, right? So I'm going to write one over three.

Let's try another one.

Say I have 625, and I've taken that to the fourth root.

And I want to write this and index form.

What am I going to do? What's my base? 625.

And what's my power? Well, I've got the four there, so it is to a quarter.

It is now time for your independent tasks.

So I want you to pause your video, and attempt every single question on your worksheet.

And then once you're done resume and we'll go over the questions together.

Okay, let's go over the answers together.

So, I want eight raised to the power of a third.

I have written that as the cube root of eight.

So therefore what's the cube root of eight? A number that I can times by itself three times to give me eight.

And that number is two.

Next one.

I am going to write square root of 49 and that is seven.

This here, I am going to find the cube root of 125.

And that is five.

To find the square root of 225.

That is 25.

Find a quarter, so I'm going to write four, to show that it's a quarter of one.

Well, one times, one times, one times one is one.

Here, I am finding the square root of nine, and that is three.

So checking your work, making sure you've got in the same thing and correcting your work as well.

For the next one then we've got, write each of the following in index form.

So for the first one, I want you to write it in index form.

That means I need a base raised to the power of something.

Well, this is just a square root symbol.

So it's asking for m raised to a half.

And this is going to be the same but with y instead raised to a half.

This is going to be z raised to a 3rd.

This is going to be d raised to a 7th because I've got a seven outside there.

And this is going to be f raised to a 9th.

Arrange the following in order the smallest first.

Well, let's evaluate each one.

25 to a half is the same as finding the square root of 25 which is five.

27 raised to a third is the same as finding the cube root of 27, which is a three.

And then 36 raised to a half is the same as finding the square root of 36, which is six.

So I'm going to put, my final is going to be 27 to a third, 25 to a half, and 36 to a half.

How did you get on with those questions? It is now time for your explore task.

How many ways can you place three unique digits? That means the numbers you use in your boxes must not repeat themselves.

So that x is an entity.

So that x a whole number.

I'm going to go through one example with you, and you're going to get a chance to find as many different ways as you can.

So that the number, so that x is an integer.

So the first one that comes to mind is two, seven and a third.

So three unique numbers two, seven and three.

So 27 raised to a third would give me three.

So my x is an integer three.

So you have a go now.

Pause your screen.

How many different ways can you, how many different ways can you come up with a number that, how many different ways can you place three unique digits in the boxes, so that x is an integer? So pause your screen now and attempt this.

And once you're done, press resume to carry on with the lesson.

Okay.

Amazing.

We have now reached the end of today's lesson.

I hope you found today's lesson fun, engaging, interesting, and everything good.

And don't forget to complete the quiz before you go.

And I will see you at the next lesson.