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.

Literal Numbers

Addition of Literals

Subtraction of Literals

Multiplication of Literals

Properties of Multiplication of Literals

Division of Literals

Powers of Literal Numbers






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