Table of Contents
-3984 cubed, (-3984)3, is the number you get when multiplying -3984 times -3984 times -3984.
It can also be looked at as exponentiation involving the base -3984 and the exponent 3.
The term is usually pronounced 3rd power of negative three thousand nine hundred eighty-four or negative three thousand nine hundred eighty-four cubed.
The cube of -3984 is a perfect cube because the number is the product of the three equal integers -3984.
It can be written as -3984 × -3984 × -3984 or in exponential form.
Read on to learn everything about the number negative three thousand nine hundred eighty-four cubed, including useful identities.
Calculator
-3984 × -3984 × -3984 = -63,235,067,904
The inverse operation of cubing -3984 is extracting the cube root of -3984, explained here.
In the next section we elaborate on the cube -3984.
What is -3984 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length -3984 has an area of -63,235,067,904.
The sum and the differences of two cubes, for example with side length -3984 and -3985, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = -3984, b = -3985 and the equivalence we get:
(-3984)3 = -7969 x (-39842 – -3984 × -3985 + -39852) – -39853 = -7969 x (15872256 – 15876240 + 15880225) – -63282696625 = -7969 x 15876241 – -63282696625 = -63,235,067,904 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = -3984, b = -3985 and the equivalence we get:
(-3984)3 = (-39842 + -3984 × -3985 + -39852) + -39853 = 15872256 + 15876240 + 15880225 + -63282696625 = -63,235,067,904
As follows from (1), -3984 cubed can be calculated from -3985 cubed and -3984 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(-3984)3 = (2 × -3984 – 1) × (-39842 – -3984 + 1) – (-3985)3 = -7969 × (15872256 – -3985) – -63282696625 = -7969 × 15876241 – -63282696625 = -63,235,067,904
Using the second formula -3984 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(-3984)3 = -39853 + 3 × -39842 – 3 × -3984 + 1 = -63282696625 + 3 × 15872256 – 3 × -3984 + 1 = -63282696625 + 47616768 – -11952 + 1 = -63,235,067,904
If you want to calculate the cube of any number, not only integers like three thousand nine hundred eighty-four, you can use our calculator above.
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A cube similar to -3984 is, for example: cube of -3986.
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The following table contains the cubes of numbers close to -3984.
Table
| Number | Cube |
|---|---|
| -3989 | -63,473,450,669 |
| -3988 | -63,425,726,272 |
| -3987 | -63,378,025,803 |
| -3986 | -63,330,349,256 |
| -3985 | -63,282,696,625 |
| -3984 | -63,235,067,904 |
| -3983 | -63,187,463,087 |
| -3982 | -63,139,882,168 |
| -3981 | -63,092,325,141 |
| -3980 | -63,044,792,000 |
| -3979 | -62,997,282,739 |
Negative Three Thousand Nine Hundred Eighty-Four Cubed
You now know everything about the cube -3984 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
-3984 cubed is equivalent to -63,235,067,904.
If you were searching for what is -3984 cubed in math or if you typed whats -3984 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube-3984, and -3984 to the 3rd power, just to name a few more examples people are often looking for.
Note that you can also find many perfect cubes including -3984 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
-3984 cubed = -3984 x -3984 x -3984 = (-3984)3 = -3984 to the 3rd power = -63,235,067,904.
The exponentiation form is mostly used to denote -3984 cube.
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– Article written by Mark, last updated on November 26th, 2023