# 2 to the 45th Power

Welcome to 2 to the 45th power, our post about the mathematical operation exponentiation of 2 to the power of 45.

If you have been looking for 2 to the forty-fifth power, or if you have been wondering about 2 exponent 45, then you also have come to the right place.

The number 2 is called the base, and the number 45 is called the exponent. In this post we are going to answer the question what is 2 to the 45th power.

## What is 2 to the 45th Power?

2 to the 45th power is conventionally written as 245, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 2^45.

245 stands for the mathematical operation exponentiation of two by the power of forty-five.

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

2 to the 45th power = \underbrace{ {\rm 2 \times\thinspace ... \times\thinspace 2} }_{\rm 45 \thickspace times} The exponent of the number 2, 45, also called index or power, denotes how many times to multiply the base (2).

Thus, we can answer what is 2 to the 45th power as

2 to the power of 45 = 245 = 3518 4372088832.

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

To stick with 2 to the power of 45 as an example, insert 2 for the base and enter 45 as the index, also known as exponent or power.

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

2 to the 45th 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 45 power, along with instructions how to use the search form, located in the sidebar or at the bottom, to obtain a number like 2^45.

## 2 to the Power of 45

Reading all of the above, you already know most about 2 to the power of 45, 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 45, 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 45th power, (245)−1, is. The inverse is the 45th root of 245, and the math goes as follows:

(245)−1
= \sqrt{2^{45}}
= 2^{45/45}
= 2^{1}
= 2

Because the index of 45 is not a multiple of 2, which means odd, in contrast to even numbers, the operation produces only one value: (245)−1 = 2.

Make sure to understand that exponentiation is not commutative, which means that 245 ≠ 452, and also note that (245)-1 ≠ 2-45, the inverse and reciprocal of 245, respectively.

You already know what 2 to the power of 45 equals, but you may also be interested in learning what 2 to the negative 45th power stands for.

Next is the summary of our content.

## Two to the Forty-fifth Power

You have reached the concluding section of two to the forty-fifth power = 245. Two to the forty-fifth power is, for example, the same as 2 to the power 45 or 2 to the 45 power.

Exponentiations like 245 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 45, what is 2 to the 45 power, 2 exponent 45 or 45 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