3 to the 2nd Power

Welcome to 3 to the 2nd power, our post about the mathematical operation exponentiation of 3 to the power of 2.

If you have been looking for 3 to the second power, or if you have been wondering about 3 exponent 2, then you also have come to the right place.

The number 3 is called the base, and the number 2 is called the exponent. In this post we are going to answer the question what is 3 to the 2nd power.

Keep reading to learn everything about three to the second power.

What is 3 to the 2nd Power?

3 to the 2nd power is conventionally written as 32, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 3^2.

32 stands for the mathematical operation exponentiation of three by the power of two.

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

3 to the 2nd power = \underbrace{ {\rm 3 \times\thinspace ... \times\thinspace 3} }_{\rm 2 \thickspace times}

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The exponent of the number 3, 2, also called index or power, denotes how many times to multiply the base (3).

Thus, we can answer what is 3 to the 2nd power as

3 to the power of 2 = 32 = 9.

If you have come here in search of an exponentiation different to 3 to the second power, or if you like to experiment with bases and indices, then use our calculator below.

To stick with 3 to the power of 2 as an example, insert 3 for the base and enter 2 as the index, also known as exponent or power.

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

3 to the 2nd 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 2 power, along with instructions how to use the search form, located in the sidebar or at the bottom, to obtain a number like 3^2.

3 to the Power of 2

Reading all of the above, you already know most about 3 to the power of 2, 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 2, 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 2nd power, (32)−1, is. The inverse is the 2nd root of 32, and the math goes as follows:

= \sqrt[2]{3^{2}}
= 3^{2/2}
= 3^{1}
= 3

Because the index of 2 is a multiple of 2, which is even, in contrast to odd numbers, the operation produces two results: (32)−1 = \pm 3; the positive value is the principal root.

Make sure to understand that exponentiation is not commutative, which means that 32 ≠ 23, and also note that (32)-1 ≠ 3-2, the inverse and reciprocal of 32, respectively.

You already know what 3 to the power of 2 equals, but you may also be interested in learning what 3 to the negative 2nd power stands for.

Next is the summary of our content.

Three to the Second Power

You have reached the concluding section of three to the second power = 32. Three to the second power is, for example, the same as 3 to the power 2 or 3 to the 2 power.

Exponentiations like 32 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 2, what is 3 to the 2 power, 3 exponent 2 or 2 power of 3, 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 32, then check out the articles which you can locate in the header menu of our site.

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