Rule Of Exponents – Everything You Need To Know

In mathematics, among its many formulas and rules, is the rule of exponents. On some occasion you have had to see exponentiated numbers or with exponents.

In fact, in the day to day of each person, you can find yourself having to use a calculation with exponents. Yes, you can do them in another way, but it can take much longer to do the calculations, when the exponent will be very simple. You will stop doing calculations with additions to change it for multiplications. Take the calculator if it is easier for you to solve them and during exam times at universities and many institutes, they will surely let you take it.

Instructions

1. Operations involving exponents are always done with repetitive calculations. Among them they can occur with divisions, multiplications, additions and even subtractions. The exponents are those numbers that always appear next to a number (small and tall).
2. The exponent will always mean that it is the number of times that should be calculated.
3. Put correctly, the words exponents and the factor will be used. What is each thing?
4. The exponent is the number that appears small and to the right of the number at the top.
5. When you say the base, you are referring to the factor.
6. If we see a figure and/or number as an exponent, what does it want to tell us? That it has to be calculated with the number that it will always have on its left side. In fact, it will have to be calculated with that number.
7. A simple and clear example. Suppose there is a number 2 and right next to it (its exponent) is a number three. What would we do then? Well, the calculation would have to be the following.
8. We would either do this: 2 + 2+ 2. We will repeat the two as many times as the exponent indicates. If it is a three in the example, the exponent will tell us that it has to be done three times. If it were a two, twice, a five, five times, a ten, ten times… and so on, whatever they tell us. Doing the calculation of the exponent, it would be a six. Because the sum of the exponents does not give six.
9. It is also done faster. And to do it, you have the multiplications. Thanks to that, instead of making a sum, it multiplies. You don’t do 2+ 2 + 2, but you change it and you do 2 x 3. The result is the same. He’ll give us a six. When talking about empowerment, which I’m sure you’ll hear or read when you’re studying it, it’s referring to how it multiplies, always following the factors and in a summarized and/or abbreviated way.
10. When talking about exercises or operations of this type, the initials and names must be taken into account:
11. The base will always be represented as: a.
12. When talking about the exponent, it will be represented as: m.
13. In order to represent the power, it will be represented as: b.
14. Within these options, of how to decipher or do operations with exponents, there are five types of laws. The first, the second, the third, the fourth and the fifth law.
15. We summarize what each law consists of and what you are going to find with each one of them. The first law, for example, comes to explain that the powers that have the same base must be operated by multiplying the power, taking into account that the base must always be different from zero and the same base will be left and the value will be raised. exponent. To better reflect, a simple example.
16. Let’s imagine, for example, the following case: 2 and the exponent would be 4. How would we calculate it? As follows. We would do this: 2 x 2x 2 x 2= 16. Why? Remember what we told you above. The exponent, always, comes to tell us the times that must be repeated in an operation. Therefore, if we have said that the exponent is four, it is telling us that it is four times. What number should it be? If we have said that 2, then what is multiplied is that number times the exponent.
17. Now let’s see, the second law. This law tells us that the quotient must always be the power that has the same base. We remind you or, we tell you, that saying a quotient will always be saying the same thing as doing a division.
18. How do we do this type of operation? We will have to look at the powers. They have to be based on the same number. What will be the difference? The exponents, which then they do, can be different.
19. Now we go to the third law. It is related to powers. Here you have to do operations on the powers. That is, imagine that they can be powers that are zero and others that are not. If they have the same powers as a base or do not have the same powers.
20. The fourth law. This law is related to the products of power. When in a number the power is the same as that of the factors with the same exponent.
21. The fifth law, let’s get to it. When we see a fraction that has a power that is either equal or higher, it has the numerator as its numerator and then you look and you also see the same denominator, and even the same exponent.
22. We have already told you what laws you can find, also how the exponents are and even how the exponents are deciphered. It remains to be discussed then, when there are fractions that have parentheses how they have to be solved. If you find figures that are in parentheses and also have an exponent, the exponent changes the value and now rules over the rest of the data and figures.
23. When a power is going to be raised, it will have to be calculated by multiplying the exponent.
24. If you see an exponent that turns out to be no longer positive and is now negative, that is, it has the subtraction sign, don’t be scared. You will have to make a different calculation, but of course, it will have to be calculated the same and without problems.
25. When you come across an exponent that is not positive and is the other way around, from negative (-) to positive (+) you always have to change the signs to convert them.
26. The exponent notations are made up of two parts… on the one hand there is what is called the base (which we already discussed) and on the other, there is what is called the notation. The base always look at what it is, the number that is at the bottom and instead, the notation, is the number that is located on the side in small. For this reason, it is the same as saying the exponent (which it is). It will always be the small number that is attached to the large number and the large one is on its left side (if you have any doubts, look at this detail, it will help you a lot).
27. If you come across exponents that turn out to be positive, you will see it or you will be able to know that it is so, because either it is not indicated with any sign (it does not need to have the sign of the sum because it is already taken for granted) or they can be negative. which can also be understood as having to be calculated using division as a method of calculation.

What do you need:

1. A sheet of paper, a notepad or notebooks to do the calculations.
2. A pencil, pen or label.
3. An eraser or tipex.
4. A scientific calculator so that I can help you.

Tips

When talking about the rule of exponents, basically you don’t have to be scared. It is referring, above all, to the calculations that are specified or have to do, with all the operations that have exponents between their numbers and/or figures. They can be of two types: both negative and positive. If you do not understand the procedure, if it seems difficult for you to know how to perform the operations, in short, everything that has to do with numbers and mathematics is difficult for you, we would like to tell you that there are many options to remedy it.

One of them is to look in notebooks and/or books and write down how to do it and how to follow the steps to decipher it or get the operations. Of course, there is that of hiring a private teacher. Help you with the operations, explain it to you well, make you understand it and you can do it for yourselves. But if you want to have the same result and also, you can’t or don’t want to pay anything, the most viable option will be to watch YouTube videos online or Google to follow teachers who explain it to you just as well but completely free of charge. Above all, in mathematics as in any subject that costs you or you cannot keep up with it, you have to spend more hours than the norms, especially as they say “dig in” and study and practice. Do not throw in the towel… in these exercises it is vital that you practice and do not stop doing exercises based on trial and error. Go testing, delete if necessary and start over. But don’t leave it lying around.