# 2 to the 32nd Power

Welcome to 2 to the 32nd power, our post about the mathematical operation exponentiation of 2 to the power of 32.

If you have been looking for 2 to the thirty-second power, or if you have been wondering about 2 exponent 32, then you also have come to the right place.

The number 2 is called the base, and the number 32 is called the exponent. In this post we are going to answer the question what is 2 to the 32nd power.

## What is 2 to the 32nd Power?

2 to the 32nd power is conventionally written as 232, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 2^32.

232 stands for the mathematical operation exponentiation of two by the power of thirty-two.

As the exponent is a positive integer, exponentiation means a repeated multiplication:

2 to the 32nd power = \underbrace{ {\rm 2 \times\thinspace ... \times\thinspace 2} }_{\rm 32 \thickspace times} The exponent of the number 2, 32, also called index or power, denotes how many times to multiply the base (2).

Thus, we can answer what is 2 to the 32nd power as

2 to the power of 32 = 232 = 4294967296.

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

To stick with 2 to the power of 32 as an example, insert 2 for the base and enter 32 as the index, also known as exponent or power.

Next, hit the convert button, then check the result.

2 to the 32nd 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 32 power, along with instructions how to use the search form, located in the sidebar or at the bottom, to obtain a number like 2^32.

## 2 to the Power of 32

Reading all of the above, you already know most about 2 to the power of 32, 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 32, 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 32nd power, (232)−1, is. The inverse is the 32nd root of 232, and the math goes as follows:

(232)−1
= \sqrt{2^{32}}
= 2^{32/32}
= 2^{1}
= 2

Because the index of 32 is a multiple of 2, which is even, in contrast to odd numbers, the operation produces two results: (232)−1 = \pm 2; the positive value is the principal root.

Make sure to understand that exponentiation is not commutative, which means that 232 ≠ 322, and also note that (232)-1 ≠ 2-32, the inverse and reciprocal of 232, respectively.

You already know what 2 to the power of 32 equals, but you may also be interested in learning what 2 to the negative 32nd power stands for.

Next is the summary of our content.

## Two to the Thirty-second Power

You have reached the concluding section of two to the thirty-second power = 232. Two to the thirty-second power is, for example, the same as 2 to the power 32 or 2 to the 32 power.

Exponentiations like 232 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 32, what is 2 to the 32 power, 2 exponent 32 or 32 power of 2, then it’s safe to assume that you have found your answer as well.

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Posted in Powers of 2