# 10 to the Negative 82nd Power

Welcome to 10 to the negative 82nd power, our post about the mathematical operation exponentiation of 10 to the power of -82.

If you have been looking for 10 to the negative eighty-second power, or if you have been wondering about 10 exponent minus 82, then you also have come to the right place.

The number 10 is called the base, and the number minus 82 is called the exponent. In this post we are going to answer the question what is 10 to the negative 82nd power.

Keep reading to learn everything about ten to the negative eighty-second power.

## What is 10 to the Negative 82nd Power?

10 to the negative 82nd power is conventionally written as 10-82, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 10^-82.

10-82 stands for the mathematical operation exponentiation of ten by the power of negative eighty-two.

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

10 to the negative 82nd power = \frac{1}{\underbrace{ {\rm 10 \times\thinspace ... \times\thinspace 10} }_{\rm 82 \thickspace times}} The absolute value of the exponent of the number -82, 82, denotes how many times to multiply the base (10), and the power’s minus sign stands for reciprocal.

Thus, we can answer what is 10 to the negative 82nd power as

10 to the power of minus 82 = 10-82 = 1 / 100 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000.

If you have come here in search of an exponentiation different to 10 to the negative eighty-second power, or if you like to experiment with bases and indices, then use our calculator below.

To stick with 10 to the power of negative 82 as an example, insert 10 for the base and enter -82 as the index, aka exponent or power.

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

10 to the negative 82nd power is an exponentiation which belongs to the category powers of 10.

Similar exponentiations on our site in this category include, but are not limited, to:

Ahead is more info related to 10 to the negative 82 power, along with instructions how to use the search form, located in the sidebar or at the bottom, to obtain a number like 10 to the power negative 82.

## 10 to the Power of -82

Reading all of the above, you already know most about 10 to the power of minus 82, 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, 10 to the power minus 82, and you will be taken to a result page with relevant posts.

Now, we would like to show you what the inverse operation of 10 to the negative 82nd power, (10-82)−1, is. The inverse is the 1 over the 82nd root of 1082, and the math goes as follows:

(10-82)−1
= \frac{1}{\sqrt{10^{82}}}
= \frac{1}{10^{82/82}}
= \frac{1}{10^{1}}
= \frac{1}{10}

Because the index -82 is a multiple of 2, which means even, in contrast to odd numbers, the operation produces two results: (10-82)−1 = pm \frac{1}{10}; the positive value is the principal root.

Make sure to understand that exponentiation is not commutative, which means that 10-82 ≠ -8210, and also note that (10-82)-1 ≠ 1082, the inverse and reciprocal of 10-82, respectively.

You already know what 10 to the power of minus 82 equals, but you may also be interested in learning what 10 to the 82nd power stands for.

Next is the summary of negative 82 power of 10.

## Ten to the Negative Eighty-second Power

You have reached the final part of ten to the negative eighty-second power. Ten to the negative eighty-second power is the same as 10 to the power minus 82 or 10 to the minus 82 power.

Exponentiations like 10-82 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 10 power -82, what is 10 to the negative 82 power, 10 exponent minus 82 or 82 negative power of 10, then it’s safe to assume that you have found your answer as well.

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Posted in Powers of 10