-4000 Cubed

-4000 cubed, (-4000)³, is the number you get when multiplying -4000 times -4000 times -4000.

It can also be looked at as exponentiation involving the base -4000 and the exponent 3.

The term is usually pronounced 3rd power of negative four thousand or negative four thousand cubed.

The cube of -4000 is a perfect cube because the number is the product of the three equal integers -4000.

It can be written as -4000 × -4000 × -4000 or in exponential form.

Read on to learn everything about the number negative four thousand cubed, including useful identities.

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(-4000)³ = -64,000,000,000
-4000 × -4000 × -4000 = -64,000,000,000
The inverse operation of cubing -4000 is extracting the cube root of -4000, explained here.

In the next section we elaborate on the cube -4000.

What is -4000 Cubed?

A cube is a three-dimensional shape with 6 equal square faces.

Hence, a cube with side length -4000 has an area of -64,000,000,000.

The sum and the differences of two cubes, for example with side length -4000 and -4001, can be calculated with the following formulas:

1. a³ + b³ = (a + b) × (a² – ab + b²) ⇔ a³ = (a + b) × (a² – ab + b²) – b³
   With a = -4000, b = -4001 and the equivalence we get:
   (-4000)³ = -8001 x (-4000² – -4000 × -4001 + -4001²) – -4001³ = -8001 x (16000000 – 16004000 + 16008001) – -64048012001 = -8001 x 16004001 – -64048012001 = -64,000,000,000
2. a³ – b³ = (a – b) × (a² + ab + b²) ⇔ a³ = (a – b) × (a² + ab + b²) + b³
   With a = -4000, b = -4001 and the equivalence we get:
   (-4000)³ = (-4000² + -4000 × -4001 + -4001²) + -4001³ = 16000000 + 16004000 + 16008001 + -64048012001 = -64,000,000,000

As follows from (1), -4000 cubed can be calculated from -4001 cubed and -4000 squared using the identity:

n³ = (2 × n – 1) × (n² -n + 1) – (n-1)³
(-4000)³ = (2 × -4000 – 1) × (-4000² – -4000 + 1) – (-4001)³ = -8001 × (16000000 – -4001) – -64048012001 = -8001 × 16004001 – -64048012001 = -64,000,000,000

Using the second formula -4000 cubed can be also be computed with this identity:

n³ = (n-1)³ + 3n² -3n + 1
(-4000)³ = -4001³ + 3 × -4000² – 3 × -4000 + 1 = -64048012001 + 3 × 16000000 – 3 × -4000 + 1 = -64048012001 + 48000000 – -12000 + 1 = -64,000,000,000

If you want to calculate the cube of any number, not only integers like four thousand, you can use our calculator above.

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A cube similar to -4000 is, for example: cube of -2.


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The following table contains the cubes of numbers close to -4000.

Table

Negative Four Thousand Cubed

You now know everything about the cube -4000 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:

-4000 cubed is equivalent to -64,000,000,000.

If you were searching for what is -4000 cubed in math or if you typed whats -4000 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube-4000, and -4000 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 -4000 cubed using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

-4000 cubed = -4000 x -4000 x -4000 = (-4000)³ = -4000 to the 3rd power = -64,000,000,000.

The exponentiation form is mostly used to denote -4000 cube.

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– Article written by Mark, last updated on November 26th, 2023