Bilangan Berpangkat (3) - Bilangan Berpangkat Pecahan, Bentuk Akar - Matematika SMP

Hello friends, see you again with me on the Legurless channel. In this video we will continue our study of the divisible number. We will learn about divisible numbers. First, don't forget to subscribe to the Legurless channel, the button is at the bottom right. And later on the top right, I usually give a playlist so that you can immediately learn the divisible numbers from beginning to end.

So we have learned positive and negative numbers. It turns out that a number can also have a split number. This split number is the same as a negative number, it cannot be rationally divided, so it enters the incorrect number. Actually, the split number of a number can be changed into the root and vice versa.

So the shape is like this. So if you have the root of the y-thousand from the x-thousand of a, then a is x-thousand of a-thousand of x-thousand of y. If the opposite is true, it means this is the inside-thousand, so a-thousand of x is the root of this, so the inside-thousand is the inside-thousand. Like that. Instead of being confused, let's just try it. Usually the problem is to change it into the root shape.

For example, I have a number 2, a number 1, 3, 4. I'm told to change it to a root. Later, we usually change this fraction, this number of fractions, to a root. Usually, we will use this formula. Why can we use this formula, sir? Besides this formula, of course. This is to manipulate a little so that the process is easier. Later, I will explain.

So if you meet like this, actually the most common step is you change it into two units, how many? So it's a normal division, 7/4. Then you use the first formula that we just added. So you have 2/7 root of 4. So it turns out that this can be simplified, it can come out of the root into 2

root of 4 from 2 to the 3rd. Where did you get it? 2 to the 7th is 2 to the 4th times 2 to the 3rd, which can be derived from this. Actually, there is one step that is quite interesting, which is as follows. So, I will change it into a form like this. 2 to the 1st plus 3 to the 4th.

This first column, we can go back here now. So I have 2x2x3/4. Now the rest is just this. This is 2x2x4/2x3. So the bottom is the root column, the third is the denominator. The result is the same, so we can use two ways.

What is the advantage? The advantage will be in negative digits. Let's try the B first. This means that I can write it as 3/2 + 1/3. So this is 3/2 * 3/3. Which means that what we need to do is this. So I have 3/2 * root of 3, below it.

from 3 to the power of 1. This is the upper part, the denominator. Done. The steps are faster. Later, if we find the minus, we will use this method, it's easier.

Why is it easier? Because if we use this first method, we will deal with the form of the root. So, for example, I make it 1/7 ^ 4/5, then we make it and so on. Actually, we can think like this. For this one, so you have to remember, this is a very helpful way. I now have 7

Because it's -41/5, I'm looking for a lower minus, which means -5. But how much does it have to be added to get back like this? Added 4/5. Right, -5 + 4/5 is -41/5. Here, I now have 7 -5 times 7/4/5.

So here I have 1/7/5 times the root of 5/7/4. Done. Faster. So if you use the first method, you have to make 1/7/4/5. Then you make it a normal fraction. 1/7/21/5.

Make the root, 1/ root of 5, from 7 to the 21. Later, I have to rationalize it again. Well, it's confusing, right? Long. This one is shorter. Let's try for D. Minus 5, the lowest point of this. Minus 4. Oh, there's no minus here. 5 to the -4. Added 1/3.

So I have minus, plus minus again. 5 minus 4 times 5 times 1 times 3. This means 1 times 5 times 4 times the root of 3 times 5 times 1. So it's easier to change it.

if we change from the form of a fraction to a root number. Now we will try the next one, we will try to change a form into a fraction. What does it mean? It means we want to change it to, for example, 2 times half

multiplied by 3/4 and so on. So everything is above and the number can be divided. So if we meet a situation like this, we see that 16 is still a normal number, we change it to a prime factor. This is 2/4, then I have 2/4 multiplied by root of 5,

per 1 per 2 square root 2. So this 2 wants to go up. It wants to come out of the root, it has to go up first. So I have 2 square root 4, square root 5, 2 square root minus 2. Then it comes out of the root. So I have 2 square root 4 times 2 square root minus 2 square root 5.

So the final result is 2/3 3/5. Now, I want to teach you a way to make it a little faster. So the fastest way, the principle is like this. So if you have the root of Y from A to the X, actually, this is X divided by Y, or you can call it A to the X times 1/Y.

So, this root form is also possible to write as 1/y. If this is multiplied, if a number of units is multiplied, the form becomes the same as this. This can be like this. So it's the same, actually the concept is the same. It means in a problem like this, we can do this. 2/4 multiplied by 2, we want to take care of these two.

First, it's below, it wants to go up, so it was 2/2 times -1. Then, after going up, it wants to exit the root, which means it's multiplied by 1/5. So here, I have 2/4 times 2/-2/5.

The answer is, multiply the number of digits. 2 to the 3rd, 3 to the 5th. So we save 2 steps. Now let's try this one. So we will take it out of the root and we want the shape to be times x to the 3rd times y to the 3rd. Let's see the x first.

-2 is divided by 2/3, which means multiplied by 2/3, and the root of 5 is multiplied by 1/5. Then we see this, the y. y is divided by 3, and divided by 2/3, which means multiplied by 2/3, multiplied by 1/5. So this can be corrected. This cannot be simplified. I have x.

This means -4/15 times y^2/5. This is the answer. So it's only up to here. So the step is faster. Well, this method doesn't work or can't be used if the shape is suddenly like this. Added. Well, we can't use the way to jump. Usually we call it the way to jump or jump rope.

We can't use it. So it must be in this form, not in the plural form. If there is a plural form, it is related to the algebra. So it must be factored and so on. Now let's try the C. We will collect the x and the y. There are x and y, so let's try to complete the x first. The front is not affected, the middle is multiplied by this.

x to the power of 1/6, up to the power of -1, so it was broken down, it will rise up, then this is multiplied by 2, it will be multiplied by 2. Now this x has to be careful, it is divided, this is divided, it means if multiplied it becomes x 3/4 divided by y 1/4, the position is changed.

then the other x remains 3/4. Then for y, here we have y^2, y^2 * 2, y^1 / 4 * -1. We finish this first, because it's still blue, I'll use the blue one first, times y^2 *

y -1/4 here kakak means you have x ^ 2 * x ^ -1/6 1/3 here there are two times x ^ 3/4 means the final result if it is multiplied then we use this formula where x ^ 2 + -1/3 + 3/4

times y, which is the middle, plus half, minus 1/4. This means that the denominator is equated to x/12, so here I have 6, plus times minus, plus 9. This y means 1 minus 1/4, 3/4. Then the final answer is x

11/12, 6-4=2, 2+9=11, times y = 3/12. So it's quite easy. Now let's try to continue. Usually the next question is like this. So for this question, we will be asked to form the form in the form of a positive and non-separate bracket. It means it can be root, or it must be root, because there should not be a separable bracket.

Then the rank must be positive, which means it must be corrected first. And this one is not allowed. This rank must also be gone. There must be no negative rank. So if we encounter a problem like this, we will use the same method as before. We will use the jump-and-go method. Then we will make it until the end, until it looks like this. Then we will make it into a form of a value.

Let's try it. So we have the number 2 here, divided by minus 2, 2 divided by minus 2. Let's work on the upper one first. B divided by half, divided by minus 2, means multiplied by minus 2. A comes out of the root, that is half, multiplied by minus 2. Now I want to work on the lower one. This A is different, I give a different color. A.

-5 goes up, which means multiplied by -1, multiplied by -2, which means multiplied by -2. So you know why multiplied by -2 again, because it's multiplied by multiplied, which means multiplied. b is -6 goes up, which means multiplied by -1, multiplied by -2, which means multiplied by -2. Then, the 2, 2 comes out of the root,

the middle point, go up by minus 1, then multiplied by minus 2. Now we simplify it first. This is 2 minus 2 times b minus 1 times a minus 1. Here I have a, which means this is minus 10 times b minus 12 minus 6 times minus 1 plus 6 times minus 2 minus 12 times 2

minus 1. If it's done, then we will work on each one. For the number 2, 2 minus 2 times 2 minus 1 means 2 minus 2 plus minus 1. For the number a, a minus 1 times a minus 10 means plus minus 10. For the number b, b minus 1 times b minus 12 means plus minus 12.

So here I have 2 -3 times a -11 times b -13. It means if we want a positive value without a break, it has to go down. So 1/2 -3

times a to the minus 11 times b to the 13th. This is plus, it's down. What formula is this? The formula for number 2. Remember, if it goes up or down, we multiply it by minus 1. Let's try the last one, this shape. If we find a shape like this, we work on this a first until it's done. It means a to the minus 1/2

out of the root of the minus 3, which means multiplied by 1/3 multiplied by b, this is 3, 1/2 we make it into a normal fraction, 7/2 multiplied by 1/3 because it comes out of the root of the 3rd square. Now we want to do this, a, the 1/2 square is 3/2, out of the root of the 2nd square, which means multiplied by 1/2,

then it will come out again from the root of the third, so 1/3. b means -4/3 times, comes out of the root of the second, comes out of the root of the third. Now, we just calculated this, this means, I'll calculate the orange first. This is kakak has a, the third can be subtracted, 1/4. This is b, the fourth can be subtracted, the rest 2.

which means -2/3. Meanwhile, for this one, I have a -1/6 times b 7/6. This is a little bit wrong, it should be 9. If so, then we just work it out. It means I have a -1/6 times b 7/6 minus 2/9.

So, this is equated with the denominator, so it becomes a^2 + 3^12 * b^3 = 18 6 to 18 * 3, 7 is also multiplied by 3, 21. Minus 4/18. So, here I have a^1 *

D, what's the number? 17/18. This is not finished yet, because the number is positive here, fortunately, but there is still a gap. We can do this as follows. It becomes root of 12/a times root of 18/b^17.

Actually, it's done here, but the appearance is not good. Then we can do more. Here, you can equate the name from the rank. For example, to be the KPK search, it means 36, it means 3, multiplied by B rank, it means 34/36, 18 is 36 multiplied by 2, 17 is also multiplied by 2.

So this can be the root of 36, so it becomes A ^ 3 times B ^ 34. This is the final result.

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