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-3998 cubed, (-3998)3, is the number you get when multiplying -3998 times -3998 times -3998.
It can also be looked at as exponentiation involving the base -3998 and the exponent 3.
The term is usually pronounced 3rd power of negative three thousand nine hundred ninety-eight or negative three thousand nine hundred ninety-eight cubed.
The cube of -3998 is a perfect cube because the number is the product of the three equal integers -3998.
It can be written as -3998 × -3998 × -3998 or in exponential form.
Read on to learn everything about the number negative three thousand nine hundred ninety-eight cubed, including useful identities.
Calculator
-3998 × -3998 × -3998 = -63,904,047,992
The inverse operation of cubing -3998 is extracting the cube root of -3998, explained here.
In the next section we elaborate on the cube -3998.
What is -3998 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length -3998 has an area of -63,904,047,992.
The sum and the differences of two cubes, for example with side length -3998 and -3999, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = -3998, b = -3999 and the equivalence we get:
(-3998)3 = -7997 x (-39982 – -3998 × -3999 + -39992) – -39993 = -7997 x (15984004 – 15988002 + 15992001) – -63952011999 = -7997 x 15988003 – -63952011999 = -63,904,047,992 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = -3998, b = -3999 and the equivalence we get:
(-3998)3 = (-39982 + -3998 × -3999 + -39992) + -39993 = 15984004 + 15988002 + 15992001 + -63952011999 = -63,904,047,992
As follows from (1), -3998 cubed can be calculated from -3999 cubed and -3998 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(-3998)3 = (2 × -3998 – 1) × (-39982 – -3998 + 1) – (-3999)3 = -7997 × (15984004 – -3999) – -63952011999 = -7997 × 15988003 – -63952011999 = -63,904,047,992
Using the second formula -3998 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(-3998)3 = -39993 + 3 × -39982 – 3 × -3998 + 1 = -63952011999 + 3 × 15984004 – 3 × -3998 + 1 = -63952011999 + 47952012 – -11994 + 1 = -63,904,047,992
If you want to calculate the cube of any number, not only integers like three thousand nine hundred ninety-eight, you can use our calculator above.
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A cube similar to -3998 is, for example: cube of -4000.
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The following table contains the cubes of numbers close to -3998.
Table
| Number | Cube |
|---|---|
| -4003 | -64,144,108,027 |
| -4002 | -64,096,048,008 |
| -4001 | -64,048,012,001 |
| -4000 | -64,000,000,000 |
| -3999 | -63,952,011,999 |
| -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 |
Negative Three Thousand Nine Hundred Ninety-Eight Cubed
You now know everything about the cube -3998 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
-3998 cubed is equivalent to -63,904,047,992.
If you were searching for what is -3998 cubed in math or if you typed whats -3998 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube-3998, and -3998 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 -3998 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
-3998 cubed = -3998 x -3998 x -3998 = (-3998)3 = -3998 to the 3rd power = -63,904,047,992.
The exponentiation form is mostly used to denote -3998 cube.
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– Article written by Mark, last updated on November 26th, 2023