Powers and Exponents - Free Educational videos for Students in K-12 | Lumos Learning

Powers and Exponents - Free Educational videos for Students in k-12


Powers and Exponents - By Anywhere Math



Transcript
00:0-1 Mhm . I've got three friends who really like to
00:02 shop . And each of those friends have three bags
00:04 in each bag . Or three shirts . And he
00:07 sure has three buttons . How many buttons and all
00:28 . Welcome to anywhere . Math . I'm Jeff Jacobson
00:30 And today we are talking about powers and exponents .
00:33 Okay , let's talk about all those buttons . So
00:37 if we remember we had three friends , Okay ,
00:40 Each of those friends had three bags . Now ,
00:44 if you want to figure out , well how many
00:46 bags total ? You would just do three times three
00:48 . So we are multiplying . That gives us the
00:51 number of bags . But in each bag had three
00:54 shirts to find the number of shirts . Again ,
00:56 we multiply that by three but we don't want the
00:59 number of shirts . We want the number of buttons
01:02 and there were three buttons on each shirt . So
01:05 we're going to multiply that again by three . So
01:08 if we want to know the total number of buttons
01:10 , it's just three times three times three times three
01:12 . Which is this is nine times three is 27
01:16 times three is 81 . So our final answer is
01:20 81 buttons , which is a lot of buttons .
01:25 Now , instead of writing three times three times three
01:28 times three , which can kind of be a little
01:31 bit boring , there's a little shortcut , we could
01:34 write that another way and that is to use powers
01:37 . So instead of writing the product like this ,
01:40 we could write this product as a power and it
01:43 would look like that . Let's talk about each little
01:49 part of this power . So first , the whole
01:51 thing is uh called a power and the power is
01:59 just another way of writing the product of repeated factors
02:04 . Next , this three is called the base and
02:10 that just shows what factor is being repeated . Finally
02:16 , the four is called the exponent and an exponent
02:24 just shows how many times the base or the factor
02:28 is being repeated . Okay , so the three is
02:32 being repeated four times just like here . 1234 Okay
02:37 . Uh And all together we call that a power
02:39 . Just another way of showing repeated multiplication . It's
02:43 like a shortcut . Okay now let's talk about how
02:46 you would actually read a power . Let's stick with
02:49 three as the base . Uh So this first one
02:53 , three is the base two is the exponents .
02:55 How do you read this power ? And to as
02:58 an exponent has a special word that we use and
03:00 we say squared . So this we would read as
03:03 three squared . Okay , anytime you see a two
03:12 as an experiment you would read it as square .
03:14 Yeah . Three is also special . It has a
03:17 special name . Uh So three we call cute .
03:20 So this would be three cute and you can remember
03:28 that like three dimensions . Looks like a cube is
03:31 three dimensional . Uh Same thing . A square is
03:34 two dimensions so that can help you with that .
03:36 Um Everything else is very simple . So if the
03:41 export is four we would just say three to the
03:47 fourth . Okay , five would be three to the
03:52 5th . 63 of the 673 to the seventh and
03:56 so on and so on . The only two you
03:58 really got to make sure you remember r squared and
04:02 cubed . Okay , let's try a couple examples .
04:05 So right , each product as a power notice it's
04:09 just written as a product . We're gonna change it
04:11 to look like a power . So uh first we
04:13 see that four is what is being repeated . So
04:16 that's gonna be my face now . I just need
04:21 to count how many times it was repeated . So
04:23 12345 fours which means that is my exponents . So
04:29 four times four times four times four times four as
04:32 a power is four to the fifth . Let's try
04:34 another one . Uh Again what's being repeated ? Well
04:37 12 is being repeated 123 times that becomes my exponent
04:43 . So my answer is 12 cubed . Remember three
04:47 ? We say cube . Try a couple on your
04:50 own . Okay , let's move on to another example
04:57 . This one says evaluate each power . Well first
05:00 what does it mean to evaluate ? Well if you
05:03 look at the word , hopefully you noticed something ,
05:05 you see value . I mean I know it's not
05:08 spelled with an E . But uh basically evaluate this
05:12 means find the value of it . So this is
05:16 written as a power seven squared . We want to
05:19 find the value of that well and to do that
05:21 , we change it back to a product . So
05:24 seven squared means seven Is getting multiplied two times seven
05:30 times 7 . I'm sorry . Don't make that mistake
05:34 . Seven times seven which is 49 . That's the
05:40 value of seven squared . Uh Next five . Hopefully
05:45 you remember how to say that . Cute . five
05:48 , cute . The base is 5.5 is getting repeated
05:52 three times . Well five times 5 is 25 times
05:57 five is 125 . And that is the value of
06:03 five . Cute . Here's a couple to try on
06:05 your own . Next Let's look at this list .
06:12 149 , 16 , and 36 . The question is
06:17 , what does that what do those numbers have in
06:20 common ? You take a look that maybe you can
06:23 figure it out and if you want you can pause
06:25 and see if you can figure it out . The
06:28 thing that they have in common is they are all
06:30 perfect squares and a perfect square . Mhm . Okay
06:40 , it's just a square of a whole number .
06:43 Okay , that's all it is square of a whole
06:53 number . So for example , one is a perfect
06:57 square because one square is one , Four is a
07:03 perfect square because two squared is four , right ?
07:08 We're squaring whole numbers . 16 is a perfect square
07:11 because four squared is 16 , is a perfect square
07:16 because six squared is 36 and obviously there's an infinite
07:21 amount of perfect square . So let's try some examples
07:25 dealing with perfect squares . Okay , here's our last
07:27 example determine whether each number is a perfect square .
07:31 So the 1st 1 , 64 , is that a
07:33 perfect square ? Basically you got to think is there
07:36 a whole number When squared would equal 64 ? And
07:41 hopefully you have uh Some of your squares memorized and
07:46 hopefully you know that eight squared is equal to 64
07:51 . So 64 is a perfect square . Now ,
07:55 how about 20 same thing ? Is there a number
07:58 that we can times by itself that we can square
08:02 ? That would give us 20 The product of 20
08:05 . And hopefully you're not thinking well two times 10
08:08 . But remember you have to multiply the same number
08:10 by itself . So no , it's not right .
08:14 For squared is 16 . 4 times four is 16
08:17 , 5 squared is 25 . So there is no
08:20 number that we multiply . Uh no hole number that
08:24 we multiply by itself to get 20 . So 20
08:28 is not a perfect square . Here's some to try
08:31 on your own . Right . Thanks for watching .
08:37 And if you like this video , please subscribe .
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