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Welcome to 3 to the negative 12th power, our post about the mathematical operation exponentiation of 3 to the power of -12.
If you have been looking for 3 to the negative twelfth power, or if you have been wondering about 3 exponent minus 12, then you also have come to the right place. 🙂
The number 3 is called the base, and the number minus 12 is called the exponent. In this post we are going to answer the question what is 3 to the negative 12th power.
Keep reading to learn everything about three to the negative twelfth power.
What is 3 to the Negative 12th Power?
3 to the negative 12th power is conventionally written as 3-12, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 3^-12.
3-12 stands for the mathematical operation exponentiation of three by the power of negative twelve.
As the exponent is a negative integer, exponentiation means the reciprocal of a repeated multiplication:
The absolute value of the exponent of the number -12, 12, 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 12th power as
If you have come here in search of an exponentiation different to 3 to the negative twelfth power, or if you like to experiment with bases and indices, then use our calculator above.
To stick with 3 to the power of negative 12 as an example, insert 3 for the base and enter -12 as the index, aka exponent or power.
3 to the negative 12th 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 12 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 12.
3 to the Power of -12
Reading all of the above, you already know most about 3 to the power of minus 12, 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 12, 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 12th power, (3-12)−1, is. The inverse is the 1 over the 12th root of 312, and the math goes as follows:
Because the index -12 is a multiple of 2, which means even, in contrast to odd numbers, the operation produces two results: (3-12)−1 =
; the positive value is the principal root.
Make sure to understand that exponentiation is not commutative, which means that 3-12 ≠ -123, and also note that (3-12)-1 ≠ 312, the inverse and reciprocal of 3-12, respectively.
You already know what 3 to the power of minus 12 equals, but you may also be interested in learning what 3 to the 12th power stands for.
Next is the summary of negative 12 power of 3.
Three to the Negative Twelfth Power
You have reached the final part of three to the negative twelfth power. Three to the negative twelfth power is the same as 3 to the power minus 12 or 3 to the minus 12 power.
Exponentiations like 3-12 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 -12, what is 3 to the negative 12 power, 3 exponent minus 12 or 12 negative power of 3, then it’s safe to assume that you have found your answer as well.
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