# Exponent calculator

The exponent calculator will allow you to calculate the exponent of a power from its base and the result.

For example, imagine you want to calculate the exponent of a power of which we know that the base is 2 and the result is 8, in this case, we are multiplying the number 2 by itself a total of x times until we get to eight.

To do this calculation in our exponent tool, you simply have to enter as base the number 2 (or whatever you need to multiply by itself) and in the result field the corresponding number. When you have the data entered, press the calculate button and you will obtain the value of your power. If you want to calculate powersYou can do it in the link that we have just left you.

## How the exponent calculator works To get a good understanding of how the exponent calculator it is essential that you know what a power is and what parts it is composed of. For example, in the power 34 we can identify:

• Basecorresponds to the number 3 and refers to the number that we are going to multiply by itself n times.
• Exponentin our example it would be the number 4 and it indicates the number of times by which the base must be multiplied by itself.

That is, 34 is the same as 3 x 3 x 3 x 3 x 3 and results in 81 in both cases.

Now that you know what is a powerYou can use our calculator to obtain the exponent online without any problems.

## How to calculate the exponent of a power knowing the result

For to get the exponent of a power from its result we will have to resort to the logarithms and the following formula:

Exponent of the power = log(result) / log(base of the power)

For example, if we are asked to find the exponent of a power whose base is 3 and the result is 81, we apply the above formula and we have that:

Exponent = log 81 / log 3 = 1.91 / 0.48 = 4

Is the result we have obtained true? Let's have a look:

2 x 2 x 2 x 2 x 2 x 2 = 81 = 24

We have just demonstrated that the solution is correct. It is important, however, that in order to obtain a reliable result, a when calculating logarithms, take as many decimal places as possible. We may fall short with two or three and have rounding errors that are too high.

## Negative exponent powers

What happens if the exponent of a power is negative? In these cases, we can express it as the inverse of that power but with positive exponent. That is to say: Here are some examples of powers with negative exponent equivalently expressed by their inverse:

3-2 = 1/32

4-3 = 1 / 43

This resource is widely used to simplify powers or fractions. so remember it because you will use it in more than one math exercise.