Table of Contents
-3993 cubed, (-3993)3, is the number you get when multiplying -3993 times -3993 times -3993.
It can also be looked at as exponentiation involving the base -3993 and the exponent 3.
The term is usually pronounced 3rd power of negative three thousand nine hundred ninety-three or negative three thousand nine hundred ninety-three cubed.
The cube of -3993 is a perfect cube because the number is the product of the three equal integers -3993.
It can be written as -3993 × -3993 × -3993 or in exponential form.
Read on to learn everything about the number negative three thousand nine hundred ninety-three cubed, including useful identities.
Calculator
-3993 × -3993 × -3993 = -63,664,587,657
The inverse operation of cubing -3993 is extracting the cube root of -3993, explained here.
In the next section we elaborate on the cube -3993.
What is -3993 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length -3993 has an area of -63,664,587,657.
The sum and the differences of two cubes, for example with side length -3993 and -3994, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = -3993, b = -3994 and the equivalence we get:
(-3993)3 = -7987 x (-39932 – -3993 × -3994 + -39942) – -39943 = -7987 x (15944049 – 15948042 + 15952036) – -63712431784 = -7987 x 15948043 – -63712431784 = -63,664,587,657 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = -3993, b = -3994 and the equivalence we get:
(-3993)3 = (-39932 + -3993 × -3994 + -39942) + -39943 = 15944049 + 15948042 + 15952036 + -63712431784 = -63,664,587,657
As follows from (1), -3993 cubed can be calculated from -3994 cubed and -3993 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(-3993)3 = (2 × -3993 – 1) × (-39932 – -3993 + 1) – (-3994)3 = -7987 × (15944049 – -3994) – -63712431784 = -7987 × 15948043 – -63712431784 = -63,664,587,657
Using the second formula -3993 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(-3993)3 = -39943 + 3 × -39932 – 3 × -3993 + 1 = -63712431784 + 3 × 15944049 – 3 × -3993 + 1 = -63712431784 + 47832147 – -11979 + 1 = -63,664,587,657
If you want to calculate the cube of any number, not only integers like three thousand nine hundred ninety-three, you can use our calculator above.
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A cube similar to -3993 is, for example: cube of -3995.
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The following table contains the cubes of numbers close to -3993.
Table
| Number | Cube |
|---|---|
| -3998 | -63,904,047,992 |
| -3997 | -63,856,107,973 |
| -3996 | -63,808,191,936 |
| -3995 | -63,760,299,875 |
| -3994 | -63,712,431,784 |
| -3993 | -63,664,587,657 |
| -3992 | -63,616,767,488 |
| -3991 | -63,568,971,271 |
| -3990 | -63,521,199,000 |
| -3989 | -63,473,450,669 |
| -3988 | -63,425,726,272 |
Negative Three Thousand Nine Hundred Ninety-Three Cubed
You now know everything about the cube -3993 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
-3993 cubed is equivalent to -63,664,587,657.
If you were searching for what is -3993 cubed in math or if you typed whats -3993 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube-3993, and -3993 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 -3993 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
-3993 cubed = -3993 x -3993 x -3993 = (-3993)3 = -3993 to the 3rd power = -63,664,587,657.
The exponentiation form is mostly used to denote -3993 cube.
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– Article written by Mark, last updated on November 26th, 2023