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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