Calculate Exponents & Learn to Use Exponents in Math - [5-7-15] - Free Educational videos for Students in K-12

Calculate Exponents & Learn to Use Exponents in Math - [5-7-15] - By Math and Science

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00:00	Hello . Welcome back . The title of this lesson
00:02	is called what is an exponent ? This is part
00:05	one . So at the end of this lesson you'll
00:07	understand what an exponent is , how to write down
00:09	exponents and also how to calculate using exponents . And
00:13	I can't emphasize enough how important exponents are . We
00:16	actually use exponents in all branches of math from everything
00:21	to calculating how much gravity exists between the Earth and
00:24	the moon to calculating a magnetic field . Just so
00:28	many things building bridges , we use exponents lots and
00:31	lots of cases in math . So for us we're
00:33	gonna start at the beginning of the story and talk
00:35	about what actually is an exponent . So the idea
00:38	is the following , let's say I give you a
00:40	number two and I raise it to the power of
00:43	to like this . What does this actually mean ?
00:46	Now the bigger to down here is called the base
00:48	and the smaller one on the top is called an
00:51	exponent . Now what it actually means is an exponent
00:54	is a shortcut from multiplication . I'll say that again
00:57	. An exponent is just a shortcut for multiplication .
01:00	And what I mean by that is when you see
01:02	something written like this and I tell you in this
01:04	problem to simplify the expression , all you need to
01:07	do is take the base and multiply it by itself
01:12	two times two and you multiply it with the number
01:14	of times here that you have in the exponents .
01:16	So because this is a two in the expo it's
01:19	two times two and then of course , you know
01:21	what two times two is and you just write down
01:23	that the answer is four and that's the answer .
01:25	So if you go into a calculator or a computer
01:28	and you put two and raise it to an exponent
01:30	power of two and calculate the answer . It's going
01:33	to be the same thing as two times two ,
01:35	which is going to be the same thing as four
01:37	. So the idea is exponents allow us to write
01:41	down multiplication is when it's times itself lots of times
01:45	are very , very quickly and easily . And also
01:48	we use it very very , very often in real
01:50	life problems . Let's say we have the problem .
01:53	five raised to the power of to the power of
01:57	to is actually really , really common . It's so
01:59	common actually that we call it has a special word
02:03	. So five to the power of two or five
02:05	days to the exponent of two . We call it
02:07	squared . So if somebody tells you , hey ,
02:09	what's two squared , what's three squared ? What's four
02:13	squared ? All It means it's raised to the power
02:16	of the exponent of two . And again , there's
02:18	so many examples of that when I throw a baseball
02:21	and it makes a curved arc in the sky .
02:23	When we write down the math that describes the curved
02:26	path , we have exponents of power of two running
02:29	around all of our math that we use to calculate
02:32	things like that in real life . So here five
02:35	to the power of two means what it means .
02:37	We take the base five and we multiply it by
02:40	itself so that it's done here two times we have
02:43	two fives here because it's raised to the power of
02:45	two . Five times five as you know , is
02:49	25 . So we now know that five squared or
02:52	five to the power of two is 25 , just
02:55	like two squared . Also the same thing as two
02:57	to the power of four is sorry to to the
02:59	power of two is equal to four . All right
03:03	. These are really simple problems . Really fast problems
03:05	. Once we get the hang of it is gonna
03:06	go really fast problem . Number three , what if
03:08	I give you eight raised to the power of to
03:10	again ? So far all of the exponents have been
03:13	too . So here , what do we do ?
03:15	It just means you take the eight which is the
03:17	base and you multiply it by itself . And how
03:20	many kids do you have ? Two of them ?
03:22	And so you multiply eight times eight and you get
03:24	64 . And so we've learned that eight squared or
03:28	eight to the power of two is equal to the
03:30	number 64 . So you see the pattern , you're
03:33	just multiplying it by itself . It's eight times 85
03:36	times 52 times two . And the exponent tells you
03:39	how many times to do that . Now , here
03:41	we have a little bit of a different animal .
03:43	What if I give you the number one into the
03:45	power of three ? What do you think is going
03:47	to happen here ? Well basically what we do is
03:50	we still multiply by itself . But how many times
03:53	do we do it ? Here is a one .
03:55	Here's another one . That would be one squared but
03:57	we don't have that . We have one cubed ,
03:59	cubed is another thing . Another way of saying power
04:02	of three , so squared is power of two cubed
04:06	is power of three . Those are just words that
04:08	we have here . Since it's cube we actually have
04:10	to multiply another time because there has to be three
04:13	ones here . Since it's cubed . Now we follow
04:16	order of operations . We have multiplication , we go
04:18	left to right so one times one is one .
04:21	We still have that one left over . We just
04:23	calculated this one and now we have one times one
04:26	which again is one . So here's a bonus question
04:29	one to the power of three is what one ?
04:32	What do you think ? One to the power of
04:34	four is ? Well you just multiply by one again
04:37	you'll get a 11 to the power of five .
04:39	Still 11 to the power of seven still 11 to
04:42	the power of 1000 . Still one because multiplying by
04:45	one just doesn't really change much . Alright next problem
04:50	. Let's take a look at something a little different
04:52	. What about two to the power of three ?
04:54	Well we're multiplying again by itself . Uh Times itself
04:59	here's a two multiplied by a two . That would
05:02	be two squared but we have two cubes that we
05:04	have to have another two There again we follow order
05:07	of operations , we multiply left the right two times
05:09	two is four . We still have this times to
05:12	hear that we have to do So this was four
05:15	times to four times 2 is eight . So two
05:18	to the power of three or two cubed is 81
05:21	to the power of three or one cube is one
05:24	. All right , Let's switch back to squares .
05:28	What do you think ? Seven square it is or
05:30	seven to the power of two ? Well , again
05:33	, we always multiplied by itself . So it's seven
05:35	times seven . There's only two of them here because
05:37	it's squared . Seven times seven is 49 . So
05:41	the answer of seven squared is 49 . Okay ,
05:46	so you see the idea of experience , it really
05:48	gives a lot of students trouble , but the actual
05:51	concept is dead simple . What about 10 to the
05:55	power of 2 ? I mean , it follows the
05:57	exact same pattern every time you're multiplying times itself .
06:01	10 times . Not times to not times to 10
06:04	times 10 . You're multiplying by itself and you're doing
06:07	it two times 10 times 10 is what ? 100
06:11	so we've learned that 10 squared is equal to 100
06:14	or 10 to the power of two is equal to
06:17	100 . All right . Let's choose something a little
06:20	bit larger . What about three to the power of
06:22	three ? What do we do for that one Again
06:25	? We're always multiplying by itself . So we have
06:28	three times three . That would be three squared .
06:31	But we have one more up here . We have
06:32	to go times three again , there's three of them
06:34	here . So three times three times three . Let's
06:36	do order of operations . We have to go left
06:38	to right three times three is nine . But we
06:41	still have this times three there . What is nine
06:44	times three ? It is 27 . So , we've
06:47	learned that three to the power of three , also
06:49	called three cubed is equal to 27 . All right
06:54	. Only have a couple more problems . What about
06:56	three to the power of to well , it's very
06:59	similar to what we just did above here . We
07:02	only have a square . So it's three times three
07:04	. There's two of them here and three times three
07:06	is nine . So , we've learned that three squared
07:08	is in fact nine . All right . I think
07:14	when we have one more problem here , what about
07:18	four to the power of two or four squared ?
07:21	What is that ? Well , it's gonna be again
07:24	multiplied by itself four times four . There has to
07:27	be two of them there because it's squared and four
07:30	times four is what ? 16 . So , we've
07:32	learned that four to the power of two or four
07:34	squared is equal to 16 . I cannot tell you
07:39	how incredibly important exponents are . I don't want to
07:42	go off too much in the , in the side
07:45	in the weeds a little bit . But I'm telling
07:47	you that later . When you learn how to calculate
07:49	the gravitational force between two objects , we have exponents
07:53	in the equations right ? Which are the little squares
07:56	. In fact , it's a square that we have
07:58	in that equation . When we calculate the path of
08:00	a baseball through the air , we have squares little
08:03	powers of two in the equations . If I calculate
08:05	the electric or the magnetic field , when I talk
08:08	about radio ways , there's squares in almost all of
08:11	the equations that we actually have in real life .
08:13	So this is learning and formulating that foundation for that
08:17	. So I'd like you to go through , make
08:18	sure you understand exponents And to calculate the answers like
08:22	this . And then follow me on the part two
08:24	, we'll get a little more practice with exponents .

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