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-3997 Cubed

-3997 cubed, (-3997)3, is the number you get when multiplying -3997 times -3997 times -3997.

It can also be looked at as exponentiation involving the base -3997 and the exponent 3.

The term is usually pronounced 3rd power of negative three thousand nine hundred ninety-seven or negative three thousand nine hundred ninety-seven cubed.

The cube of -3997 is a perfect cube because the number is the product of the three equal integers -3997.

It can be written as -3997 × -3997 × -3997 or in exponential form.

Read on to learn everything about the number negative three thousand nine hundred ninety-seven cubed, including useful identities.

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(-3997)3 = -63,856,107,973
-3997 × -3997 × -3997 = -63,856,107,973

The inverse operation of cubing -3997 is extracting the cube root of -3997, explained here.

In the next section we elaborate on the cube -3997.

What is -3997 Cubed?

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

Hence, a cube with side length -3997 has an area of -63,856,107,973.

The sum and the differences of two cubes, for example with side length -3997 and -3998, can be calculated with the following formulas:

  1. a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
    With a = -3997, b = -3998 and the equivalence we get:
    (-3997)3 = -7995 x (-39972 – -3997 × -3998 + -39982) – -39983 = -7995 x (15976009 – 15980006 + 15984004) – -63904047992 = -7995 x 15980007 – -63904047992 = -63,856,107,973
  2. a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
    With a = -3997, b = -3998 and the equivalence we get:
    (-3997)3 = (-39972 + -3997 × -3998 + -39982) + -39983 = 15976009 + 15980006 + 15984004 + -63904047992 = -63,856,107,973

As follows from (1), -3997 cubed can be calculated from -3998 cubed and -3997 squared using the identity:

n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(-3997)3 = (2 × -3997 – 1) × (-39972 – -3997 + 1) – (-3998)3 = -7995 × (15976009 – -3998) – -63904047992 = -7995 × 15980007 – -63904047992 = -63,856,107,973

Using the second formula -3997 cubed can be also be computed with this identity:

n3 = (n-1)3 + 3n2 -3n + 1
(-3997)3 = -39983 + 3 × -39972 – 3 × -3997 + 1 = -63904047992 + 3 × 15976009 – 3 × -3997 + 1 = -63904047992 + 47928027 – -11991 + 1 = -63,856,107,973

If you want to calculate the cube of any number, not only integers like three thousand nine hundred ninety-seven, you can use our calculator above.

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A cube similar to -3997 is, for example: cube of -3999.


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The following table contains the cubes of numbers close to -3997.

Table

NumberCube
-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
-3992-63,616,767,488

Negative Three Thousand Nine Hundred Ninety-Seven Cubed

You now know everything about the cube -3997 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:

-3997 cubed is equivalent to -63,856,107,973.

If you were searching for what is -3997 cubed in math or if you typed whats -3997 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube-3997, and -3997 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 -3997 cubed using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

-3997 cubed = -3997 x -3997 x -3997 = (-3997)3 = -3997 to the 3rd power = -63,856,107,973.

The exponentiation form is mostly used to denote -3997 cube.

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