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 = 3
^{2}
3 × 3 × 3 = 3
^{3}
3 × 3 × 3 × 3 × 3 = 3
^{5}
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 = a
^{2}
a × a × a = a
^{3}
a × a × a × a × a = a
^{5}, and so on.
Also, we write
7 × a × a × a × a = 7a
^{4}
4 × a × a × b × b × c × c = 4a
^{2}b
^{2}c
^{2}
3 × a × a × b × b × b × c × c × c × c as 3a
^{2}b
^{3}c
^{4} and so on.
We read a
^{2} 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, a
^{5} 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 a
^{2}, a is called the base and 2 is the exponent or index.
Similarly, in a
^{5}, 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
a
^{9} = a × a × a × a……………… repeatedly multiplied 9 times.
a
^{15} = a × a × a × a……………… repeatedly multiplied 15 times.
Conventionally, for any literal a, a
^{1} is simply written as a,
i.e., a
^{1} = a.
Also, we write
a × a × a × b × b = a
^{3}b
^{2}
7 × a × a × a × a × a = 7a
^{5}
7 × a × a × a × b × b = 7a
^{3}b
^{2}
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
Algebra Page
6th Grade Page
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