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# -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.

## Calculator

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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.

Just enter your number; nothing else to be done.

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

NumberCube
-4005-64,240,300,125
-4004-64,192,192,064
-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

## 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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