# 3 to the Negative 1st Power

Welcome to 3 to the negative 1st power, our post about the mathematical operation exponentiation of 3 to the power of -1.

If you have been looking for 3 to the negative first power, or if you have been wondering about 3 exponent minus 1, then you also have come to the right place.

The number 3 is called the base, and the number minus 1 is called the exponent. In this post we are going to answer the question what is 3 to the negative 1st power.

Keep reading to learn everything about three to the negative first power.

## What is 3 to the Negative 1st Power?

3 to the negative 1st power is conventionally written as 3-1, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 3^-1.

3-1 stands for the mathematical operation exponentiation of three by the power of negative one.

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

3 to the negative 1st power = \frac{1}{\underbrace{ {\rm 3 \times\thinspace ... \times\thinspace 3} }_{\rm 1 \thickspace times}} The absolute value of the exponent of the number -1, 1, denotes how many times to multiply the base (3), and the power’s minus sign stands for reciprocal.

Thus, we can answer what is 3 to the negative 1st power as

3 to the power of minus 1 = 3-1 = 1 / 3.

If you have come here in search of an exponentiation different to 3 to the negative 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 negative 1 as an example, insert 3 for the base and enter -1 as the index, aka exponent or power.

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

3 to the negative 1st 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 negative 1 power, along with instructions how to use the search form, located in the sidebar or at the bottom, to obtain a number like 3 to the power negative 1.

## 3 to the Power of -1

Reading all of the above, you already know most about 3 to the power of minus 1, 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 minus 1, 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 negative 1st power, (3-1)−1, is. The inverse is the 1 over the 1st root of 31, and the math goes as follows:

(3-1)−1
= \frac{1}{\sqrt{3^{1}}}
= \frac{1}{3^{1/1}}
= \frac{1}{3^{1}}
= \frac{1}{3}

Because the index of 1 is not a multiple of 2, which means odd, in contrast to even numbers, the operation produces only one value: (31)−1 = \frac{1}{3}.

Make sure to understand that exponentiation is not commutative, which means that 3-1 ≠ -13, and also note that (3-1)-1 ≠ 31, the inverse and reciprocal of 3-1, respectively.

You already know what 3 to the power of minus 1 equals, but you may also be interested in learning what 3 to the 1st power stands for.

Next is the summary of negative 1 power of 3.

## Three to the Negative First Power

You have reached the final part of three to the negative first power. Three to the negative first power is the same as 3 to the power minus 1 or 3 to the minus 1 power.

Exponentiations like 3-1 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 -1, what is 3 to the negative 1 power, 3 exponent minus 1 or 1 negative 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