Power of Literal Quantities
Power of literal quantities means when a quantity is multiplied by itself, any number of times, the product is called a power of that quantity. This product is expressed by writing the number of factors in it to the right of the quantity and slightly raised.
For example:
(i) m × m has two factors so to express it we can write m × m = m2(ii) b × b × b has three factors so to express it we can write b × b × b = b3
(iii) z × z × z × z × z × z × z has seven factors so to express it we can write z × z × z × z × z × z × z = z7
Learn how to read and write the power of literal quantities.
(i) Product of x × x is written as x2 and it is read as x squared or x raised to the power 2.(ii) Product of y × y × y is written as y3 and it is read as y cubed or y raised to the power 3.
(iii) Product of n × n × n × n is written as n4 and it is read as forth power of n or n raised to the power 4.
(iv) Product of 3 × 3 × 3 × 3 × 3 is written as 35 and it is read as fifth power of 3 or 3 raised to the power 5.
How to identify the base and exponent of the power of the given quantity?
(i) In a5 here a is called the base and 5 is called the exponent or index or power.(ii) In Mn here M is called the base and n is called the exponent or index or power.
Solved examples:
1. Write a × a × b × b × b in index form.
a × a × b × b × b = a2b32. Express 5 × m × m × m × n × n in power form.
5 × m × m × m × n × n = 5m3n2
3. Express -5 × 3 × p × q × q × r in exponent form.
-5 × 3 × p × q × q × r = -15pq2r
4. Write 3x3y4 in product form.
3x3y4 = 3 × x × x × x × y × y × y × y
5. Express 9a4b2c3 in product form.
9a4b2c3 = 3 × 3 × a × a × a × a × b × b × c × c × c
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