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Potencias de números enteros - Contenido educativo

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Subido el 19 de octubre de 2023 por Carolina H.

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Potencias dse números enterosu

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Okay, what we are going to record is the class of how to make powers of whole numbers. 00:00:00
So, let's start with the first example. We know what a power is. 00:00:06
5 squared, what would it be? 00:00:10
5 by 5. 00:00:14
No, the definition of power. We are going to work only with the powers, sorry, without the final result. 00:00:16
And if I have 5 cubed, what would it be? 00:00:21
5 by 5. 00:00:24
5 by 5. 00:00:25
Vale, pues el mismo concepto de potencia lo puedo aplicar a una base, esta base que es positiva también podría tenerla, ¿de qué tipo? Ahora que estoy trabajando con heteros, negativa, entonces si yo quisiera hacer menos 5 al cuadrado tendría que coger el menos 5 entero y elevarlo al cuadrado, ¿qué sería? 00:00:25
that is minus 5 times minus 5 and as we have said that the base is minus 5, we have to multiply it 00:00:49
whole and we do the same thing we saw yesterday first we operate signs then we operate numbers what 00:01:00
happens is that normally the numbers are going to be very large and we are going to leave them in the form of 00:01:09
potencia de base positiva las potencias de base negativa siempre las voy a dejar 00:01:14
como potencias de base positiva operando el signo entonces como operaría yo estos 00:01:22
signos menos por menos más 00:01:30
las potencias lo vamos a ver como las operas pero esto sería más 5 al cuadrado 00:01:42
sólo quiero la expresión de la potencia operando el signo no vamos a trabajar 00:01:50
todavía con propiedades con potencias es lo que vamos a ver después vale las 00:01:54
We are going to see the powers later. 00:01:57
So, I would have two minus signs and I would have 5 by 5, which would be 5 squared. 00:01:59
Notice that this is what I want you to see well. 00:02:07
This is a power of base... 00:02:10
Of what sign? 00:02:16
Negative. 00:02:18
Negative. 00:02:19
This is a power of base... 00:02:24
Positive. 00:02:34
Positive. 00:02:35
Has it been clear? 00:02:36
Has everyone been clear? 00:02:39
At the moment, everyone has it clear? 00:02:41
Okay. 00:02:43
Let's see what happens 00:02:44
if I now... 00:02:45
Well, I'm not going to delete it. 00:02:48
I'm going to add a page. 00:02:52
If I now have 00:02:56
minus 5 00:02:57
raised to the cube. 00:02:58
Is this a positive or negative base power? 00:03:00
Negative. 00:03:03
Okay, because I multiply 00:03:05
Minus 5 times minus 5 times minus 5. 00:03:06
First I operate signs, only I operate signs. 00:03:12
What will I get? 00:03:14
Minus 5. 00:03:15
And then what power would I get? 00:03:17
5 times 5 times 5, what would it be? 00:03:19
5 to the cube. 00:03:21
5 to the cube. 00:03:23
This is a base power. 00:03:25
No. 00:03:28
No, it's not the same. 00:03:31
That's what I want you to see. 00:03:33
It's not the same. 00:03:35
no es lo mismo fíjate mira esto es una potencia de base positiva porque no 00:03:36
porque esto en realidad es menos 5 x 5 x 5 quien se repite el 5 es positivo o 00:03:47
negativo por eso es una potencia de base positiva este es el opuesto de una 00:03:57
power of positive base, that is, the parenthesis is only different in that if it carries parentheses it is negative, if it does not carry the positive, of course, notice that here what you are multiplying is minus 5 by minus 5 by minus 5, because when it is in the parenthesis, the 3 affects the minus, the base, the 3 affects the minus, then that is the important thing, this is what you have to distinguish well, you have to learn to see it, if I have minus 5 here 00:04:03
Elevado al cubo 00:04:31
Lo que tengo es una potencia 00:04:32
De base negativa 00:04:34
Esto de aquí 00:04:37
Es una potencia 00:04:42
De base 00:04:44
Negativa 00:04:46
Y sin embargo 00:04:48
Aquí 00:04:51
El signo ya lo he operado 00:04:52
¿Cuántos signos menos hay aquí? 00:04:54
Solo uno 00:04:56
Así que es el opuesto 00:04:57
de una potencia 00:05:00
no, de base 00:05:03
positiva 00:05:05
porque lo único que se repite 00:05:07
es el 5, y el 5 es positivo 00:05:12
entonces tengo un menos 00:05:14
y luego la potencia de 5 por 5 por 5 00:05:15
así que 00:05:17
aunque el resultado sea 00:05:19
menos 125 en ambos 00:05:22
casos, no es lo mismo 00:05:24
tener una potencia de base 00:05:26
negativa, que tener el opuesto 00:05:28
de una potencia de base 00:05:30
positive. Has it been clear? How many less signs do I have on the left? 3, 1, 2 and 3. Here I have 00:05:32
three less signs. How many less signs do I have here? 1. Have we understood it? Let's make an example. 00:05:43
And if I put this, how many less signs do you have here? 00:05:53
Two. 00:06:03
No? 00:06:04
One. 00:06:05
Why? 00:06:05
Because you have eight. 00:06:07
Develop it. 00:06:10
The two, well, I'm going to do it to the fourth, okay? 00:06:11
So I don't put a two and you don't get it wrong. 00:06:14
I'm going to do it to the fourth. 00:06:16
Develop the power. 00:06:19
What is minus two? 00:06:20
Of course, there is only one minus sign. 00:06:28
It is the opposite of a positive base power. 00:06:31
Do we understand it? 00:06:36
For it to be a negative base power, how would it have to be? 00:06:37
A parenthesis. 00:06:41
Gulli. 00:06:42
A parenthesis. 00:06:42
Perfect. 00:06:44
For it to be a negative base power, I would have to have minus 2 to the fourth. 00:06:45
I would have to have a parenthesis outside. 00:06:52
outside that took the sign with which I would have minus 2 by minus 2 by minus 2 by minus 2 00:06:55
how many signs I have less 4 how many signs I have less above 1 we see the difference this is what 00:07:08
normally you do not see or mali the one that gives me the same does not mean that it is the same 3 by 4 00:07:19
me da lo mismo que 6 por 2? Vale, pero es lo mismo tener 3 grupos de 4 que tener 2 grupos de 6? 00:07:26
Que mi resultado sea equivalente no significa que las dos cosas sean iguales. Son expresiones 00:07:37
equivalentes, son expresiones que valen lo mismo, pero tengo cosas diferentes y eso es lo que tienes 00:07:44
que aprender a ver en el lado de la izquierda hacia arriba yo lo que tengo 00:07:50
es una el opuesto de una potencia de base negativa de una potencia de base 00:07:55
positiva mientras que yo tengo aquí el menos dos a la cuarta es una potencia de 00:08:00
base negativa vale mira para que te hagas una idea arriba 00:08:05
por fa si esto es dos a la cuarta 00:08:13
Esto es menos 2 a la cuarta. 00:08:20
¿Te acuerdas? 00:08:26
Y en este caso, el menos 2 a la cuarta, ¿dónde estaría? 00:08:30
¿A la izquierda o a la derecha? 00:08:36
Menos 2 a la cuarta. 00:08:39
A la derecha. 00:08:42
Menos 2 a la cuarta. 00:08:44
Porque da positivo. 00:08:47
Menos por menos por menos por menos da positivo. 00:08:49
Fijaos como lo he dicho, y además es que se nota, escuchadlo, porque se notan las palabras en castellano 00:08:52
Si yo digo aquí, digo menos dos a la cuarta 00:08:59
Si yo digo esto, digo menos dos a la cuarta 00:09:04
La pausa no está en el mismo sitio 00:09:11
Así que yo no lo transcribo al lenguaje matemático de la misma manera 00:09:14
minus 2 to the fourth is this on the left minus 2 to the fourth I have the opposite of 2 to the fourth 00:09:19
while if I do minus 2 to the fourth it is minus 2 times minus 2 times minus 2 times minus 2 has been 00:09:29
Is that clear? All of you? Ok, let's practice a little bit. 00:09:37
If I had... 00:09:45
Minus two to the fifth, how many minus signs do I have? 00:10:01
One. 00:10:04
1, 1, so is it a positive or negative power base? 00:10:06
Positive. 00:10:11
Positive, so it will always give positive even if it is raised to 5. 00:10:12
It will always give positive, and with the minus in front, its opposite. 00:10:15
So it will be minus 2, by 2, by 2, by 2, and by 2. 00:10:19
And if I do minus 2 to the fifth, how many minus signs do I have? 00:10:25
5, minus 2. 00:10:33
2, this board sometimes, minus 2, by minus 2, by minus 2, by minus 2, by minus 2, 5 signs less. 00:10:35
I'm going to put it in the numerical line so that you can see it clearer. 00:10:52
Look, if this is my numerical line, here I have the 0, here I will have 2 to the 5th. 00:10:55
¿Dónde estará menos 2 a la quinta? 00:11:04
Al otro lado. 00:11:08
Tendré 2 a la quinta con el menos delante, que es este. 00:11:10
Entiendo cuando dicen es un 0 a la izquierda. 00:11:16
¿Vale? 00:11:18
Y ahora, si yo quisiera menos 2 a la quinta, en este caso, ¿cuántos signos menos tengo? 00:11:19
Un momento, Gerson. 00:11:26
¿Cuántos signos menos tengo? 00:11:27
En menos. 00:11:28
Aquí, en el segundo. 00:11:29
Pues, ¿qué me va a dar el resultado? 00:11:32
Positivo. 00:11:33
positive or negative? positive 00:11:33
minus by minus? plus 00:11:35
by minus? minus 00:11:37
by minus? plus 00:11:39
so it will give me here 00:11:41
but it depends on the exponent 00:11:43
of course, if the exponents are even 00:11:45
as I can group both of them 00:11:47
and they are positive 00:11:49
it will be positive 00:11:51
if I group them in an odd way 00:11:53
I will always get a loose minus 00:11:55
so it will be negative 00:11:57
but be careful 00:11:59
The power is of a negative base, because if it is of a positive base, it always gives me a positive one. 00:12:01
Is it clear? 00:12:09
But how does the positive base work? 00:12:11
No, no, no. I mean, if the power is of a positive base, like this one, the result is always positive. 00:12:13
And if I add a minus, it will be negative. 00:12:19
But because I have the opposite of a positive base power. 00:12:21
A positive base power is always positive. 00:12:24
If then I add a minus, the result will be negative, but the power of the positive base, 2x2x2x2x2, is always something positive, even if you multiply it 5 times, 4 or 3. 00:12:29
Is it clear? 00:12:42
Another thing is if the power is of negative base, because if the power is of negative base, depending on the number of times you multiply it, the result will be positive or negative, and then if I add another minus, it will change sign. 00:12:44
sign. So what we are going to do is practice with this. I'm going to put 00:12:56
expressions that have a minus number and you're going to tell me how many minuses there are 00:13:01
to know later what the result is going to be. Has it been clear? Gerson, your 00:13:06
question. 00:13:11
Yes, it is. Let's see how it works. 00:13:13
Easy. 00:13:20
This is the parenthesis. 00:13:21
This one, yes. 00:13:24
It is to take the negative with 1 itself. 00:13:25
Of course, because it's within the power, so this 5 here affects the 2, this 5 here is affecting the 2, that's why I have 5 2s, but it's also affecting the negative, that's why I have 5 minus. 00:13:29
But the ones above, for example, don't have a minus. 00:13:53
No, because it doesn't have a parenthesis, that's why I only have a minus sign. 00:13:56
no menos. Eso es. ¿Lo has entendido? Vale, pues yo os voy a poner expresiones y me vais 00:13:59
a decir, compienso, preparo y enseño, ¿cuántos signos menos hay? Depende de lo que digas. 00:14:09
Claro, yo os coloco aquí un número y vosotros decís cuántos signos menos hay. Compienso, 00:14:16
¿Pienso, preparo y enseño? ¿De acuerdo? ¿Pienso? ¿Pienso? ¿Preparo? ¿Enseño? 1, 0, 3, 2, 2, 2. 00:14:21
Vamos a ver, vamos a desarrollarlo. 00:14:47
Este menos está aquí. 00:14:50
Este 2, ¿a quién afecta? 00:14:51
Al menos 3. 00:14:55
Al menos 3. 00:14:57
Este 2 está encima de un paréntesis. 00:15:00
Luego está afectando al 3 y está afectando al menos. 00:15:04
Por tanto, lo que yo estoy repitiendo es menos 3. 00:15:08
¿Cuántos signos menos hay? 00:15:16
It's the opposite of a negative base power. 00:15:19
But if you can't change it before doing the power? 00:15:24
Okay, good question, because you do it a lot. 00:15:27
This is the mistake you have. 00:15:30
Could you multiply this by this first? 00:15:32
Yes. 00:15:34
Yes or no? 00:15:36
I think... 00:15:37
Like this, with the finger up, if yes, 00:15:39
with the finger down, if no. 00:15:42
Can I do that for that and put that it's more, 00:15:43
and then 3 squared? 00:15:47
I think, I prepare, I teach. 00:15:49
I say yes. 00:15:54
Yes, no. 00:15:55
Gelson, why not? 00:15:56
Because we only look more. 00:15:58
Jenny, why not? 00:16:05
Because in the hierarchy of operations the power is first. 00:16:08
But 52... 00:16:13
Of course, but if I do minus by minus, I'm doing a multiplication, and what do you have to do first? 00:16:15
So the power goes first, first I have to raise to the square the minus 3, which would be 9, and with the minus in front, minus 9. 00:16:22
Is it clear? So, why did Pablito get a 0? 00:16:32
Why did he make a mistake with the hierarchy? 00:16:37
What you have to see first is that you have to do the power of the sign first, before multiplying the sign. 00:16:39
So you can't do the minus by the minus, what you have here in front. 00:16:51
This cannot be done. What you have to do is first raise the minus two times. 00:16:55
That's why you have two minus signs, plus the minus here, three. 00:17:02
It's going to be negative 00:17:06
Has it been clear? 00:17:08
For everyone? 00:17:10
I'm going to erase this 00:17:14
That's right 00:17:15
If it were raised to the cube it would be positive 00:17:19
I don't know why it doesn't erase 00:17:22
As before 00:17:26
Well, I'm going to erase the board 00:17:28
So, look 00:17:30
We had put minus 3 squared 00:17:34
And those are 00:17:37
Minus 3 by minus 3 00:17:38
So, in total, it will be three less signs. What will I get? Negative or positive? If they are three? Negative. 00:17:41
Negative. And then the power of the numbers. First, but signs, then but numbers, and I leave it in the form of power. 00:17:50
This is already a power, the opposite of a positive base power. We are going to do it with minus three to the cube, as Willy has said. 00:17:58
Willy, lo pongo a la quinta, ¿vale? 00:18:06
Para que sea más fácil. 00:18:12
Para que no haya otro tres y no se equivoquéis. 00:18:16
¿Cuántos signos menos tengo aquí? 00:18:19
¿Pienso? 00:18:21
¿Lo tenéis? 00:18:25
¿Preparo? 00:18:26
¿Ensaño? 00:18:27
Muy bien, seis. 00:18:29
Seis, seis, seis. 00:18:31
Claro que hay seis. 00:18:34
¿Cuántos signos menos? 00:18:35
¿Cuántos signos menos tienes? 00:18:36
Si dejas el móvil, a lo mejor te enteras. 00:18:39
Mira, el menos, menos. 00:18:41
Y ahora, menos tres, ¿cuántas veces? 00:18:44
Cinco. 00:18:47
Cinco. 00:18:48
Así que, ¿cuántos signos menos tienes en total? 00:18:50
Seis. 00:18:59
El resultado que te va a dar, positivo o negativo. 00:19:00
¿De qué potencia? 00:19:05
¿Tres cuántas veces? 00:19:08
Has it been clear? 00:19:09
But I'm not doing it because I do less by less. 00:19:15
I'm doing it because I do the minus five times first and then I do the opposite. 00:19:18
Have we understood it? 00:19:26
Have we understood it? 00:19:28
All of us? 00:19:31
Once you learn it, this is very easy. 00:19:33
First you copy the negative and then you do the positive. 00:19:40
Otra más. 00:19:45
¿Y si yo tengo...? 00:19:50
Vamos a ver. 00:20:07
Tranquilos. 00:20:09
Solo hay que ver primeros signos, luego números. 00:20:11
¿Cuántos signos menos tengo en total? 00:20:14
¿Pienso? 00:20:17
En toda la ecuación. 00:20:18
¿En todo? 00:20:19
¿Pienso? 00:20:21
¿Preparo? 00:20:26
Enseño. 00:20:29
¿Cuatro? 00:20:30
¿Tres? 00:20:31
¿Cuatro? 00:20:32
Cuatro, cuatro, cinco, cuatro, cuatro. 00:20:33
Ah, no, que no falta el de abajo. 00:20:35
¿Cuántos hay? 00:20:37
Cuatro. 00:20:38
Cuatro. 00:20:38
Fíjate, esto es, si lo desarrollo, arriba tendría un menos y luego menos tres por menos tres. 00:20:40
Y abajo, menos y cinco. 00:20:51
Así que, cuatro signos, menos por menos, más, y menos por menos, más, y menos por más, más. 00:20:54
Así que el resultado me va a dar más, y arriba, ¿qué potencia me va a quedar? 00:21:04
Tres, el de abajo. 00:21:09
¿Y abajo? 00:21:11
Cinco, el de abajo. 00:21:13
Pues ya está. 00:21:14
No fue tan difícil si yo sé cuántos signos menos tengo, ¿lo veis? 00:21:15
I only have to know how many minus signs I have and then place the operation of the numbers. 00:21:19
I don't understand. 00:21:24
Okay. 00:21:25
Why then, I mean, the first one is minus by minus and why then that result is not multiplied by the minus 3? 00:21:26
And this minus here? 00:21:34
It is multiplied by the minus by... 00:21:35
Please, please, please, don't talk. 00:21:37
And the minus here? 00:21:40
No, yes, but you have done... 00:21:41
Minus by minus? 00:21:44
More. 00:21:46
And by minus? 00:21:47
Between minus. 00:21:48
Between minus? 00:21:49
Ah, okay. 00:21:50
Ah, I got it. 00:21:51
Okay. 00:21:52
Okay. 00:21:53
It's just that I have paired them by pairs, I don't care. 00:21:54
You can pair them by pairs. 00:21:57
Every time you work with two minus signs multiplied or divided, what does it give you? 00:21:59
Minus by minus? 00:22:04
More. 00:22:05
And minus between minus? 00:22:06
More. 00:22:07
More. 00:22:08
More. 00:22:09
Okay? 00:22:10
Is it clear? 00:22:11
Yes. 00:22:12
So I have plus 3 squared by 5. 00:22:13
¿Dudas? 00:22:17
Una más difícil. 00:22:19
Venga. 00:22:20
Pienso, preparo y enseño. 00:22:23
A ver. 00:22:25
¿Cuántos signos menos tengo? 00:22:38
¿Y cómo te lo hacemos si son más de 10 manos? 00:22:41
¿Qué te oyes? 00:22:44
Si con los pies. 00:22:45
Eso. 00:22:48
Este hombre merece la casa y todo. 00:22:50
No nos he traído hoy. 00:22:53
¿Cuántos signos menos tengo? 00:22:55
¿Pienso? 00:22:57
¿Pienso? ¿Pienso? No necesitas pies. Te lo digo yo ya. ¿Pienso? ¿Preparo? ¿Enseño? Muy bien, 10. Sí, señor. 00:22:57
Así que el resultado, fíjate, que me da igual cómo lo haga. ¿El resultado qué va a ser? ¿Positivo o negativo? 00:23:15
With 10 less signs. Positive. Positive. And now, what's going to stay above me? 3 to the 5th. 3 to the 5th. For 5. For 5. Divided. Divided. For 2. To the cube. 00:23:21
I don't know why this 00:23:41
Has it been clear? 00:23:44
If I know how many signs 00:23:52
Guys, if I know how to count 00:23:54
Mari, if I know how many signs I have 00:23:56
The rest doesn't matter to me 00:23:59
Because it will always give me positive 00:23:59
Has it been clear? 00:24:01
So I'm always going to put it 00:24:03
As a positive base power 00:24:04
Or as the opposite of a positive base power 00:24:06
I operate the signs and leave the powers 00:24:08
Has it been clear? 00:24:11
One more 00:24:13
¿Te está gustando? 00:24:14
Pues entonces 00:24:18
¿Vemos la marca? 00:24:19
¿Eh? 00:24:37
Vale 00:24:40
¿Cuántos signos menos tengo? 00:24:41
Santo Madre de Dios 00:24:45
¿No hay mano? 00:24:46
Sí, sí hay 00:24:48
¿Pienso? 00:24:49
¿Preparo? 00:24:54
I teach 9999999 very well so I'm going to stay positive negative negative 00:24:56
less and now that I'm going to stay in the fraction 00:25:06
2 to the cube by 2 to the cube by 00:25:11
3 to the 6th, between? 00:25:18
It's changing color, I don't know why. 00:25:25
And what can I do? 00:25:27
Silence, please. 00:25:31
What can I do here? 00:25:32
Add the 2 with the 2 to the 1. 00:25:38
This is a fraction, I have the same... 00:25:40
Valeria, what can you do? What have you told me? 00:25:43
Tachar. 00:25:46
Not tachar, divide between what number? 00:25:48
Up and down between? 00:25:50
3 raised to 6. 00:25:51
3 raised to 6, and then I would have 2 cubed by 2 cubed, and between 3 raised to 6, and what do I have left? 00:25:53
64. 00:25:59
What do I have left down? 00:26:00
64. 00:26:01
Aaron, I don't want the result. What do I have left down? 00:26:03
2 cubed by 2 cubed. 00:26:05
And the minus? 00:26:09
Minus 2 cubed by 2 cubed. 00:26:11
And down? 00:26:13
Nothing. 00:26:14
It's not true? 00:26:15
Just 1. 00:26:16
Ah, if I divide 3 to the sixth, between 3 to the sixth, what does it give? 00:26:16
So it will be minus, and above I will have 2 times 2 times 2 times 2 times 2 times 2. 00:26:25
How much does it give me? 00:26:33
Minus. 00:26:34
Minus, in the form of power. 00:26:35
2 to the sixth. 00:26:39
2 to the sixth. 00:26:40
Is it clear? 00:26:42
Any questions? 00:26:46
No. 00:26:47
No one? 00:26:48
Okay. 00:26:49
I'm going to stop recording now, okay? 00:26:50
Idioma/s:
es
Idioma/s subtítulos:
en es
Autor/es:
Carolina Hassmann
Subido por:
Carolina H.
Licencia:
Reconocimiento - No comercial - Sin obra derivada
Visualizaciones:
16
Fecha:
19 de octubre de 2023 - 13:06
Visibilidad:
Público
Centro:
CEPAPUB CANILLEJAS
Duración:
26′ 55″
Relación de aspecto:
1.78:1
Resolución:
1280x720 píxeles
Tamaño:
51.91 MBytes

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