# 3 to the 71st Power

Welcome to 3 to the 71st power, our post about the mathematical operation exponentiation of 3 to the power of 71.

If you have been looking for 3 to the seventy-first power, or if you have been wondering about 3 exponent 71, then you also have come to the right place.

The number 3 is called the base, and the number 71 is called the exponent. In this post we are going to answer the question what is 3 to the 71st power.

## What is 3 to the 71st Power?

3 to the 71st power is conventionally written as 371, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 3^71.

371 stands for the mathematical operation exponentiation of three by the power of seventy-one.

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

3 to the 71st power = \underbrace{ {\rm 3 \times\thinspace ... \times\thinspace 3} }_{\rm 71 \thickspace times} The exponent of the number 3, 71, also called index or power, denotes how many times to multiply the base (3).

Thus, we can answer what is 3 to the 71st power as

3 to the power of 71 = 371 = 7509 4665149797 2480394671 5958257547.

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

To stick with 3 to the power of 71 as an example, insert 3 for the base and enter 71 as the index, also known as exponent or power.

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

3 to the 71st 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 71 power, along with instructions how to use the search form, located in the sidebar or at the bottom, to obtain a number like 3^71.

## 3 to the Power of 71

Reading all of the above, you already know most about 3 to the power of 71, 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 71, 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 71st power, (371)−1, is. The inverse is the 71st root of 371, and the math goes as follows:

(371)−1
= \sqrt{3^{71}}
= 3^{71/71}
= 3^{1}
= 3

Because the index of 71 is not a multiple of 2, which means odd, in contrast to even numbers, the operation produces only one value: (371)−1 = 3.

Make sure to understand that exponentiation is not commutative, which means that 371 ≠ 713, and also note that (371)-1 ≠ 3-71, the inverse and reciprocal of 371, respectively.

You already know what 3 to the power of 71 equals, but you may also be interested in learning what 3 to the negative 71st power stands for.

Next is the summary of our content.

## Three to the Seventy-first Power

You have reached the concluding section of three to the seventy-first power = 371. Three to the seventy-first power is, for example, the same as 3 to the power 71 or 3 to the 71 power.

Exponentiations like 371 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 71, what is 3 to the 71 power, 3 exponent 71 or 71 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