maths > exponents

Representation of Cubes and Cube Roots

    what you'll learn...


In this page, cube of a number and cube root of a number are revised.



An exponent of power 3 is called cube of the number.

eg: Cube of 7 is 73=343.

The word "cube" means : the 3D shape of equal sides and 90 angles" between edges. The exponent cube is representative of "volume of the shape cube, side to the power 3".

cube root


An exponent of power 13 or the 3rd root is called cube root of the number.

eg: Cube root of 64 is 6413=643=4.


Cube of 3 is 33.

Cube root of 8 is 83=813.

finding cube root

How to find 2163?

Cube root is a form of roots. In roots, we learned to perform prime factorization to find the root.


Cube of a number : A number to the power 3 is the cube of the number.
eg: 63=6×6×6=216

Cube Root of a number : A number to the power 13 is the cube root of the number.
eg: 2163=6 as 63=216.

Finding Cube Roots : To find cube root of a number, express the number in prime factors and group the factors.

eg: 10003 =2×2×2×5×5×53 =2×5=10

Note: This method is suitable for finding cube roots resulting in integers.


The outline of material to learn "Exponents" is as follows. Note: click here for detailed outline of Exponents s

    →   Representation of Exponents

    →   Inverse of exponent : root

    →   Inverse of exponent : Logarithm

    →   Common and Natural Logarithms

    →   Exponents Arithmetics

    →   Logarithm Arithmetics

    →   Formulas

    →   Numerical Expressions

    →   PEMA / BOMA

    →   Squares and Square roots

    →   Cubes and Cube roots