# 2 to the 13th Power

Welcome to 2 to the 13th power, our post about the mathematical operation exponentiation of 2 to the power of 13. If you have been looking for 2 to the thirteenth power, or if you have been wondering about 2 exponent 13, then you also have come to the right place. The number 2 is called the base, and the number 13 is called the exponent. In this post we are going to answer the question what is 2 to the 13th power. Keep reading to learn everything about two to the thirteenth power.

## What is 2 to the 13th Power

2 to the 13th power is conventionally written as 213, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 2^13.

213 stands for the mathematical operation exponentiation of two by the power of thirteen. As the exponent is a positive integer, exponentiation means a repeated multiplication:

2 to the 13th power = $\underbrace{ {\rm 2\hspace{3px} \times\hspace{7px} …\hspace{5px} \times\hspace{3px} 2} }_{\rm 13\hspace{3px} times}$

The exponent of the number 2, 13, also called index or power, denotes how many times to multiply the base (2).

Thus, we can answer what is 2 to the 13th power as

2 to the power of 13 = 213 = 8192.

If you have come here in search of an exponentiation different to 2 to the thirteenth power, or if you like to experiment with bases and indices, then use our calculator below.

To stick with 2 to the power of 13 as an example, insert 2 for the base and enter 13 as the index, also known as exponent or power. Next, hit the convert button, then check the result.

2 to the 13th power is an exponentiation which belongs to the category powers of 2. Similar exponentiations on our site in this category include, but are not limited, to:

Ahead is more info related to 2 to the 13 power, along with instructions how to use the search form, located in the sidebar or at the bottom, to obtain a number like 2^13.

## 2 to the Power of 13

Reading all of the above, you already know most about 2 to the power of 13, except for its inverse which is discussed a bit further below in this section.

Using the aforementioned search form you can look up many numbers, including, for instance, 2 to the power 13, and you will be taken to a result page with relevant posts.

Now, we would like to show you what the inverse operation of 2 to the 13th power, (213)−1, is. The inverse is 13th root of 213, and the math goes as follows:

(213)−1
= $\sqrt{2^{13}}$
= $2^{13/13}$
= $2^{1}$
= 2

Because the index of 13 is not a multiple of 2, which means odd, in contrast to even numbers, the operation produces only one value: (213)−1$\hspace{3px} = \hspace{3px}2$.

Make sure to understand that exponentiation is not commutative, which means that 213 ≠ 132, and also note that (213)-1 ≠ 2-13, the inverse and reciprocal of 213, respectively.

You already know what 2 to the power of 13 equals, but you may also be interested in learning what 2 to the negative 13th power stands for. Next is the summary of our content.

## Two to the Thirteenth Power

You have reached the concluding section of two to the thirteenth power = 213. Two to the thirteenth power is, for example, the same as 2 to the power 13 or 2 to the 13 power.

Exponentiations like 213 make it easier to write multiplications and to conduct math operations as numbers get either big or small, such as in case of decimal fractions with lots of trailing zeroes.

If you have been looking for 2 power 13, what is 2 to the 13 power, 2 exponent 13 or 13 power of 2, then it’s safe to assume that you have found your answer as well.

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If you like to learn more about exponentiation, the mathematical operation conducted in 213, then check out the articles which you can locate in the header menu of our site.

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Posted in Powers of 2