2 to the Negative 100th Power


Welcome to 2 to the negative 100th power, our post about the mathematical operation exponentiation of 2 to the power of -100. If you have been looking for 2 to the negative hundredth power, or if you have been wondering about 2 exponent minus 100, then you also have come to the right place. The number 2 is called the base, and the number minus 100 is called the exponent. In this post we are going to answer the question what is 2 to the negative 100th power. Keep reading to learn everything about two to the negative hundredth power.

What is 2 to the Negative 100th Power

2 to the negative 100th power is conventionally written as 2-100, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 2^-100.

2-100 stands for the mathematical operation exponentiation of two by the power of negative hundred. As the exponent is a negative integer, exponentiation means the reciprocal of a repeated multiplication:

2 to the negative 100th power = $\frac{1}{\underbrace{ {\rm 2\hspace{3px} \times\hspace{7px} …\hspace{5px} \times\hspace{3px} 2} }_{\rm 100\hspace{3px} times}}$

The absolute value of the exponent of the number -100, 100, 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 100th power as

2 to the power of minus 100 = 2-100 = 1 / 1 2676506002 2822940149 6703205376.

If you have come here in search of an exponentiation different to 2 to the negative hundredth 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 100 as an example, insert 2 for the base and enter -100 as the index, aka exponent or power. Next, hit the convert button, then check the result.



2 to the negative 100th 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 100 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 100.

2 to the Power of -100

Reading all of the above, you already know most about 2 to the power of minus 100, 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 100, 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 100th power, (2-100)−1, is. The inverse is 1 over the 100th root of 2100, and the math goes as follows:

(2-100)−1
= $\frac{1}{\sqrt[100]{2^{100}}}$
= $\frac{1}{2^{100/100}}$
= $\frac{1}{2^{1}}$
= $\frac{1}{2}$

Because the index -100 is a multiple of 2, which means even, in contrast to odd numbers, the operation produces two results: (2-100)−1 = $\pm \frac{1}{2}$; the positive value is the principal root.

Make sure to understand that exponentiation is not commutative, which means that 2-100 ≠ -1002, and also note that (2-100)-1 ≠ 2100, the inverse and reciprocal of 2-100, respectively.

You already know what 2 to the power of minus 100 equals, but you may also be interested in learning what 2 to the 100th power stands for. Next is the summary of negative 100 power of 2.

Two to the Negative Hundredth Power

You have reached the final part of two to the negative hundredth power. Two to the negative hundredth power is the same as 2 to the power minus 100 or 2 to the minus 100 power.

Exponentiations like 2-100 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 -100, what is 2 to the negative 100 power, 2 exponent minus 100 or 100 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 2-100, then check out the articles which you can locate in the header menu of our site.

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