# Powers of Literal Numbers

Powers of literal numbers are the repeated product of a number with itself is written in the exponential form.

For example:

3 × 3 = 32

3 × 3 × 3 = 33

3 × 3 × 3 × 3 × 3 = 35

Since a literal number represent a number.

Therefore, the repeated product of a number with itself in the exponential form is also applicable to literals.

Thus, if a is a literal, then we write

a × a = a2

a × a × a = a3

a × a × a × a × a = a5, and so on.

Also, we write

7 × a × a × a × a = 7a4

4 × a × a × b × b × c × c = 4a2b2c2

3 × a × a × b × b × b × c × c × c × c as 3a2b3c4 and so on.

We read a2 as the second power of a or square of a or a raised to the exponent 2 or a raised to power 2 or a squared.

Similarly, a5 is read as the fifth power of a or a raised to exponent 5 or a raised to power 5 (or simply a raised 5), and so on.

In a2, a is called the base and 2 is the exponent or index.

Similarly, in a5, the base is a and the exponent (or index) is 5.

It is very clear from the above discussion that the exponent in a power of a literal indicates the number of times the literal exponent has been multiplied by itself.

Thus, we have

a9 = a × a × a × a……………… repeatedly multiplied 9 times.

a15 = a × a × a × a……………… repeatedly multiplied 15 times.

Conventionally, for any literal a, a1 is simply written as a,

i.e., a1 = a.

Also, we write

a × a × a × b × b = a3b2

7 × a × a × a × a × a = 7a5

7 × a × a × a × b × b = 7a3b2

These are the examples of powers of literal numbers.

Subtraction of Literals

Multiplication of Literals

Properties of Multiplication of Literals

Division of Literals

Powers of Literal Numbers