# Cube of a number

## Definition

The multiplication of three same numbers to obtain another number as their product is called the cube of a number.

In mathematics, three same numbers are often involved in multiplication to represent a number by the product of them. It is written in a special notation by writing the base number once but a number $3$ is displayed as its superscript to express that a number is used thrice in multiplication to obtain a number as their product.

The exponent $3$ is read as cube because a meaning of cube is three. Hence, if a number is multiplied by itself three times, the product of them is called cube of that number.

### Example

$5$ is a number and multiply three $5$ numbers to obtain the number $125$ as their product and write the relation between them in exponential form.

$5 \times 5 \times 5 = 125$

$\implies 5^{\displaystyle 3} = 125$

In this way, some numbers can be written in cube form in terms of some other numbers.

#### Terminology

A special terminology is used to read cube based exponential terms and exponential notation.

The exponential term $5^{\displaystyle 3}$ is read in four types.

1. The cube of $5$.
2. $5$ cubed.
3. $5$ raised to the power of $3$.
4. The third power of $5$.

Similarly, $5^{\displaystyle 3} = 125$ can also be read in four ways.

1. The cube of $5$ is $125$ (or) $125$ is the cube of $5$.
2. $5$ cubed is $125$ (or) $125$ is $5$ cubed.
3. $5$ raised to the power of $3$ is $125$ (or) $125$ is $5$ raised to the power of $3$.
4. The third power of $5$ is $125$ (or) $125$ is the third power of $5$.

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