Lesson video

Hello, and welcome to this lesson on expressing powers off in different bases.

For today's lesson, you'll be needing a paper and a pen, or something you could write on and with, also, if you can minimise distraction by getting into a space with less noise, and also putting your phone on silent so you don't get distracted.

Do those now and then carry on watching the video to proceed with the lesson.

Okay, for your try this task, I want you to look at the diagram on your screen and jot down patterns that you can notice.

So what patterns can you notice in this diagram.

So pause the video now and attempt this and then resume when you think you've noticed as many different patterns as you can.

Okay, what patterns did you notice? You may be tempted to think this is a number line, but it's a bit more than a number line actually, because the button numbers are being multiplied by three each time, while the top numbers are being multiplied by nine each time.

People call this an exponential model.

You've probably seen this in the news as well, the fact that a number has been multiplied by a particular number each time.

So I've seen that three to the power of zero is the same as nine to the power of zero.

Three to the power of zero is one, try that properly, and nine to the power of zero is one.

Okay, where is to get from nine to one, I multiplied just by nine, to get from three to the power of zero to three squared, I multiplied by three twice, because three times three is nine.

So to jump from my top values, I'm multiply them by just one number each time, whereas for my second value to get to a number that is expressed with different bases but the same number, I am multiplying my bottom numbers by three twice.

So take for example, three to the power of four is 81 and nine to the power of two is 81.

My base in this first example, my base is three and my power is four, whereas here my base is nine and my power is two.

So the number 81 can be expressed with different basis.

Take for example 6561.

Two ways I can express this number using base and power is three to the power of eight, three being my base and eight being my power, and a nine to the power of four, nine being my base and four being my power.

These two expressions would give me the value 6,561.

What about this one then? I've got 10 to the power of something would give me 100 squared? Well, I know that 100 squared is 10,000.

So 10 to the power of what, would give me the value of 100 squared? Yeah, it's 10 to the power of four.

So 10,000 can be expressed using a base of 100 and the power of two or a base of 10 and a power of four.

What of the second example, four cubed is four times four times four, that is 64.

What would this number be what would be my base here, a base number that when I raised to the power of two will also give me 64? It is eight.

So 64 can be expressed as four cubed and eight squared.

So, a number can be expressed with different bases.

It is now time for your independent task.

So I want you to pause the video, attempt of couple of questions on your sheet there are not that many, and then come back and we'll go for the answers together.

Okay, I wonder how you go on with that task.

I hope you were able to answer as many questions as you can, we're now going to go through the answers of first one, two the power of zero is one, so therefore four to the power of zero is also one.

Two to the power of four, two times two, times two, times four is two times two times two times two is 16, so therefore, four to the power of two also give me a value of 16.

Four to the power of four is 256, so two to the power of eight is 256.

Eight squared is 64, so therefore 64 to the power of one is 64.

Four cubed, so four times four times four is 64, so eight squared again is 64.

Okay, f, two to the power of 10 is 1024, so four to the power of five, will also give me 1024.

Okay, two to the power of nine is 512.

Eight to the power three is also 512.

100 to the power of four gives me 100 million, so I need 10 to the power of eight for that.

Eight to the power of four is 4096.

This is probably quite tricky, but 64 squared is also 4096.

10 to the power of 10 gives me one times 10 to the power of 10, and 100 to the power of five also gives me one times 10 to the power of 10.

Okay, your explore task.

Your task is to fill in the boxes and then write down what you notice.

Once you've done that, there's a question at the bottom of your screen by our student, can you guess how we could write two to the power five as four to the power of something or as eight to the power of something.

So once you fill in those boxes, you should be able to answer the question at the bottom of your screen.

If you start this and you think I'm really struggling, and I don't know what to do, just resume the video and I'll provide you with the help and then you can go back to working on it by yourself as well.

So pause the video now and attempt this, and if you need some more support, carry on watching the video.

Okay, for your support, I would suggest you start by just type in the number two times two times two times two on your calculator and how many times you times two by itself to get 4096.

I will help you out, it is 12, right? Now, go do the same for your four, four times four times four times four, well, if I times it six times, I would get the number 4096.

Do you see a pattern between the powers that it is raised to? if you do see a pattern, it should help you work out what it should be raised to and what 64 should be raised to and what 16 should be raised to.

So pause your video now and carry on working with this filling in the boxes to get the number in the middle of your screen.

Okay, we have not reached the end of today's lesson I quite enjoyed that lesson.

I thought it was quite interesting to be able to express the same value of number in different bases, and I hope you found it interesting too.

Don't forget to complete the quiz before you go, just so that you further understand it, and you show yourself what you understood from today's lesson as well and I will see you at the next lesson.