# 3 to the 22nd Power

Welcome to 3 to the 22nd power, our post about the mathematical operation exponentiation of 3 to the power of 22.

If you have been looking for 3 to the twenty-second power, or if you have been wondering about 3 exponent 22, then you also have come to the right place.

The number 3 is called the base, and the number 22 is called the exponent. In this post we are going to answer the question what is 3 to the 22nd power.

## What is 3 to the 22nd Power?

3 to the 22nd power is conventionally written as 322, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 3^22.

322 stands for the mathematical operation exponentiation of three by the power of twenty-two.

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

3 to the 22nd power = \underbrace{ {\rm 3 \times\thinspace ... \times\thinspace 3} }_{\rm 22 \thickspace times} The exponent of the number 3, 22, also called index or power, denotes how many times to multiply the base (3).

Thus, we can answer what is 3 to the 22nd power as

3 to the power of 22 = 322 = 3 1381059609.

If you have come here in search of an exponentiation different to 3 to the twenty-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 22 as an example, insert 3 for the base and enter 22 as the index, also known as exponent or power.

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

3 to the 22nd 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 22 power, along with instructions how to use the search form, located in the sidebar or at the bottom, to obtain a number like 3^22.

## 3 to the Power of 22

Reading all of the above, you already know most about 3 to the power of 22, 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 22, 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 22nd power, (322)−1, is. The inverse is the 22nd root of 322, and the math goes as follows:

(322)−1
= \sqrt{3^{22}}
= 3^{22/22}
= 3^{1}
= 3

Because the index of 22 is a multiple of 2, which is even, in contrast to odd numbers, the operation produces two results: (322)−1 = \pm 3; the positive value is the principal root.

Make sure to understand that exponentiation is not commutative, which means that 322 ≠ 223, and also note that (322)-1 ≠ 3-22, the inverse and reciprocal of 322, respectively.

You already know what 3 to the power of 22 equals, but you may also be interested in learning what 3 to the negative 22nd power stands for.

Next is the summary of our content.

## Three to the Twenty-second Power

You have reached the concluding section of three to the twenty-second power = 322. Three to the twenty-second power is, for example, the same as 3 to the power 22 or 3 to the 22 power.

Exponentiations like 322 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 22, what is 3 to the 22 power, 3 exponent 22 or 22 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