An introduction to exponents and indices - Free Educational videos for Students in K-12

An introduction to exponents and indices - By tecmath

Transcript


00:02	Good day . Welcome to this series of videos looking
00:04	at indices and crimes in this particular series . What
00:07	we're going to have a look at first off today
00:09	is indices . Then we're going to have a look
00:11	at prime numbers and composite numbers . We're going to
00:14	then move onto squares and square roots and then cubes
00:17	and cube roots in this particular lesson . What we're
00:20	going to have a look at is index notation .
00:22	So industries are very useful in everyday life because what
00:25	they do is they allow us to write very big
00:27	numbers and very small numbers a whole lot more simply
00:30	. And these come up say you are looking at
00:32	our large distances or very , very , very small
00:35	distances . So the distance from here to our very
00:37	far away star or even how big a bacteria or
00:41	something was . Because these numbers get very big and
00:44	very small . We can look at significant numbers by
00:47	using index notation . And what they then allows us
00:50	to do is it makes the calculations a whole lot
00:52	easier . So first off indices . So industries are
00:57	also called exponents orders or powers and pretty much what
01:01	they are , is they are repeated multiplication . There
01:03	a way of writing repeated multiplication . So let me
01:07	give you an example of this . Say we had
01:09	two times two times two . The way that we
01:13	could write this in index form is as follows ,
01:15	we could right 2 to the power of three .
01:19	So what have we got here ? We have two
01:20	particular partier , the two which has been multiplied by
01:23	itself . This is called the base . We have
01:27	this part up here which is how many times to
01:31	has been multiplied by itself . And this is either
01:33	called the index or the exponents or the power .
01:37	Something like this . Okay , so you've got two
01:40	parts here and that's fairly simple . Right ? So
01:42	what about we have a look at one more example
01:44	of this ? What about we have five times five
01:47	times five times five Times five times 5 . So
01:53	this is equal to , well , what's the base
01:56	here ? The base which is the number which has
01:58	been multiplied by itself . So the base as you
02:00	can see here is five . So we have five
02:04	. Now we look at how many fires have been
02:06	multiplied here . We have 123456 This is five to
02:13	the power of six . So it's pretty simple .
02:16	Right ? Let's have a look at a couple of
02:18	further examples . Okay , a bit harder . Now
02:21	say we were to have three to the power of
02:23	four and we would multiply this by three to the
02:26	power of three . What would this be equal to
02:30	? So we can work this out . Three to
02:32	the power of four here is equal to three times
02:36	three times three times three . And we're multiplying this
02:41	boy three to the power of three . So this
02:43	is three times three times three . And as you
02:47	see here , we're multiplying these two sets of numbers
02:49	. So what does this leave us with ? Well
02:51	, pretty simply . What base have we got ?
02:53	We have a base here of three . How many
02:57	times is it being multiplied by itself ? 1234567 This
03:02	is three to the power of seven . So you
03:05	might look at a bit of a short cut here
03:06	and say , hey , what we did here is
03:08	we could just go through and add these two numbers
03:11	together . So this is three and this is four
03:13	plus three . What about this ? Say we were
03:16	in brackets to have this where we're going to go
03:18	four squared to the power of three . And what
03:22	is this equal to ? So what we could do
03:25	is we could go through and we're working this out
03:27	and we could say , okay , what we have
03:29	here is four squared four squared is four times 44
03:33	multiplied by itself twice . And we're doing this three
03:36	times . So we have four times four . We
03:39	have four times four And we have four times 4
03:43	. Okay , Because this whole part here has been
03:46	raised to this power and we're multiplying these guys .
03:49	So what's our answer here ? This is equal to
03:52	? Well , our base is for and we're multiplying
03:56	it by itself 123456 times . Okay . One last
04:03	example . What about this ? What about we go
04:06	three times four squared and see what this is equal
04:11	to . So if we were to do this once
04:13	, you can see is you can say , okay
04:14	, what we have here is we have three times
04:17	for and we're multiplying this by three times four .
04:22	So if we were to do this , what do
04:23	we end up with ? Well , we end up
04:25	with three times four times three times four . Now
04:32	, how can we write this a lot more simply
04:35	? Well , we have this number here , which
04:36	is a base three . So we have two of
04:39	those . So it's three multiplied by itself two times
04:43	to this . We're multiplying four base , which has
04:47	also got to lots here . So four squared .
04:50	So , another way of writing three times four in
04:53	brackets squared is three squared times four squared . Anyway
04:58	, hopefully that some help of you and we'll get
05:01	on very soon to the next idea which is going
05:02	to be having a look at prime numbers . All
05:04	right , see you .

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