2 to the Negative 45th Power

Welcome to 2 to the negative 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 negative forty-fifth power, or if you have been wondering about 2 exponent minus 45, then you also have come to the right place.

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

Keep reading to learn everything about two to the negative forty-fifth power.

What is 2 to the Negative 45th Power?

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

2-45 stands for the mathematical operation exponentiation of two by the power of negative forty-five.

As the exponent is a negative integer, exponentiation means the reciprocal of a repeated multiplication:

2 to the negative 45th power = \frac{1}{\underbrace{ {\rm 2 \times\thinspace ... \times\thinspace 2} }_{\rm 45 \thickspace times}}

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The absolute value of the exponent of the number -45, 45, denotes how many times to multiply the base (2), and the power’s minus sign stands for reciprocal.

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

2 to the power of minus 45 = 2-45 = 1 / 3518 4372088832.

If you have come here in search of an exponentiation different to 2 to the negative 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 negative 45 as an example, insert 2 for the base and enter -45 as the index, aka exponent or power.

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


2 to the negative 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 negative 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 to the power negative 45.

2 to the Power of -45

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

(2-45)−1
= \frac{1}{\sqrt[45]{2^{45}}}
= \frac{1}{2^{45/45}}
= \frac{1}{2^{1}}
= \frac{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 = \frac{1}{2}.

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

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

Next is the summary of negative 45 power of 2.

Two to the Negative Forty-fifth Power

You have reached the final part of two to the negative forty-fifth power. Two to the negative forty-fifth power is the same as 2 to the power minus 45 or 2 to the minus 45 power.

Exponentiations like 2-45 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 negative 45 power, 2 exponent minus 45 or 45 negative power of 2, then it’s safe to assume that you have found your answer as well.

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If you like to learn more about exponentiation, the mathematical operation conducted in 2-45, then check out the articles which you can locate in the header menu of our site.

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