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
From Powers of Literal Numbers to HOME PAGE
Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.