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 = 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 × 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
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.
Working Rules for Power Literal:
Step I: Take any variable, say 'a'.
Step II: Multiple the variable two times or three times
i.e., m × m is written as m2 (called 'm squared')
or m × m × m = m3 (called 'm cubed').
Step III: In m5 m is the base and 5 is the exponent.
NOTE:
1. Instead of writing a1 write a only.
2. The product of a and b can be written as a × b or ab.
Solved Examples on Powers of Literal Numbers:
1. Find out the base and exponent of the following:
(i) p2
(ii) t7
(iii) 54
Solution:
(i) ln p2, p is the base and 2 is the exponent.
(ii) In t7, t is the base and 7 is the exponent.
(iii) In 53, 5 is the base and 4 is the exponent.
Properties of Multiplication of Literals
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