POWER and ELEMENTS concept

Welcome back to another math lesson from a TEACHER. On this occasion, we are pleased to present you the concept of power and its elements. As is customary for us, we will start by presenting you with some basic concepts of the subject and then doing some exercises to complete the lesson. To do this, we are going to start with the basic concept of power and the elements that make up this operation. Without further ado, let's get to it.

A power it's a type of multiplication, since it is the multiplication of a number by the same, as many times as the exponent indicates. In other words, it is a way of representing a multiplication in abbreviated way. We will see this in greater depth with the examples in the following sections.

Power elements

As we have mentioned in previous lines, the power is made up of several elements.

• First of all, you will find the basis of power, which is the number that visually looks the largest.
• Then we have the exponent (also known as an index or power), which is located above and to the right of the base number and with a smaller size.
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• Exactly the number of the exponent tells us how many times should we multiply the base number by itself.

So that you can better observe what is explained in the previous sections, we leave you this simple example of a power so that you appreciate the nature of this operation.

For example:

2³

In this case, the base of the power is the number 2 Y its exponent is the number 3. According to the revised theory, the operation consists of multiplying the base number by itself, as many times as the exponent indicates. Therefore, in this case the operation would be to multiply the number 2 three times. Consequently, if we break down the power, the operation would look like this:

2³ = 2 x 2 x 2 = 8

Before continuing with the examples, in a Teacher we always consider it important that you are very attentive and focused when carrying out operations with power; since in many cases, we can get confused with the exponent and the base and multiply them automatically, this is a very common mistake in this topic.

For example: in many cases, as you are used to multiplication, you can think that the result of the previous example is 6 because you associate that the base and the exponent are multiplied. Therefore, we recommend that at the beginning you write the operation, breaking down the power in a multiplication, as we have indicated in the example. We continue.

Another example:

3² = = 3 x 3 = 9

In this case, the base number is 3 and the exponent is 2. Which means that we must multiply the number 3 by itself twice.

Let's see this case:

1⁵ = = 1 x 1 x 1 x 1 x 1 = 1

In this operation, as you can see, the base number is 1 and the exponent is 5, so we must multiply the number 1 by itself five times. And since we already know that every number multiplied by 1, it is not modified, because the result of the multiplication is 1.

This previous example helps us to introduce another important concept from this lesson; and it is that if in a power the base is 1, the result of the operation will always be 1, no matter what its exponent is.

Let's go with the last example:

3⁰ = 1

As our teacher Cristina points out in the video of the lesson, in this example the result is 1, because it has established as a norm, then at the time of any evaluation you must learn it by heart in case it appears in some exercise.

Likewise, we encourage you to continue practicing and if you have any questions, you can consult any content on our website, we will be there to help you with whatever you need.

If you watch the video you will understand much better what is a power Y what is an element, since We explain different examples.

In addition, we have left you some printable exercises with their solutions to reinforce everything explained in this video about powers. You can download it and do it at home to see if, really, you have understood the lesson that we have explained to you.