# 3 to the 52nd Power

Welcome to 3 to the 52nd power, our post about the mathematical operation exponentiation of 3 to the power of 52.

If you have been looking for 3 to the fifty-second power, or if you have been wondering about 3 exponent 52, then you also have come to the right place.

The number 3 is called the base, and the number 52 is called the exponent. In this post we are going to answer the question what is 3 to the 52nd power.

## What is 3 to the 52nd Power?

3 to the 52nd power is conventionally written as 352, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 3^52.

352 stands for the mathematical operation exponentiation of three by the power of fifty-two.

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

3 to the 52nd power = \underbrace{ {\rm 3 \times\thinspace ... \times\thinspace 3} }_{\rm 52 \thickspace times} The exponent of the number 3, 52, also called index or power, denotes how many times to multiply the base (3).

Thus, we can answer what is 3 to the 52nd power as

3 to the power of 52 = 352 = 64610 8188922667 3298932241.

If you have come here in search of an exponentiation different to 3 to the fifty-second power, or if you like to experiment with bases and indices, then use our calculator below.

To stick with 3 to the power of 52 as an example, insert 3 for the base and enter 52 as the index, also known as exponent or power.

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

3 to the 52nd power is an exponentiation which belongs to the category powers of 3.

Similar exponentiations on our site in this category include, but are not limited, to:

Ahead is more info related to 3 to the 52 power, along with instructions how to use the search form, located in the sidebar or at the bottom, to obtain a number like 3^52.

## 3 to the Power of 52

Reading all of the above, you already know most about 3 to the power of 52, 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, 3 to the power 52, and you will be taken to a result page with relevant posts.

Now, we would like to show you what the inverse operation of 3 to the 52nd power, (352)−1, is. The inverse is the 52nd root of 352, and the math goes as follows:

(352)−1
= \sqrt{3^{52}}
= 3^{52/52}
= 3^{1}
= 3

Because the index of 52 is a multiple of 2, which is even, in contrast to odd numbers, the operation produces two results: (352)−1 = \pm 3; the positive value is the principal root.

Make sure to understand that exponentiation is not commutative, which means that 352 ≠ 523, and also note that (352)-1 ≠ 3-52, the inverse and reciprocal of 352, respectively.

You already know what 3 to the power of 52 equals, but you may also be interested in learning what 3 to the negative 52nd power stands for.

Next is the summary of our content.

## Three to the Fifty-second Power

You have reached the concluding section of three to the fifty-second power = 352. Three to the fifty-second power is, for example, the same as 3 to the power 52 or 3 to the 52 power.

Exponentiations like 352 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 3 power 52, what is 3 to the 52 power, 3 exponent 52 or 52 power of 3, then it’s safe to assume that you have found your answer as well.

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Posted in Powers of 3