Download Laws of Exponents

Concept Notes/ Classes 7,8,9
Introducing Exponents
In what follows, the expression “any number” for base means natural number or zero or integer
or fraction or decimal or rational number or ‘other’ numbers.
1
The First Definition of Exponents is as follows:
If a is any number and k is any natural number other than 1 then the product
a . a . a . a . ... k times is written as 𝒂𝒌 and read as ‘a power k’.
2
The Second Definition of Exponents is as follows:
If a is any number, 𝒂𝟏 is defined to be a.
3
The Third Definition of Exponents is as follows:
If a is any number other than zero, 𝒂𝟎 is defined to be 1.
4
The Fourth Definition of Exponents is as follows:
If a is any number other than zero and k is any natural number then 𝒂−𝒌 is defined to
be the reciprocal of 𝒂𝒌 .
5
The Fifth Definition of Exponents is as follows :
𝟏
If a is any number and k is any natural number then 𝒂𝒌 is the number which when
multiplied by itself k times gives a, provided such number exists.
6
The Multiplication Rule of Exponents is as follows :
If a is any positive number and x, y are any ______then product of 𝒂𝒙 & 𝒂𝒚 is 𝒂𝒙+𝒚 .
7
The Power Rule of Exponents is as follows :
If a is any positive number and x, y are any ______________ then (𝒂𝒙 )𝒚 is 𝒂𝒙𝒚 .
8
The Distributive Rule of Exponents is as follows:
If a , b are any positive numbers and x is any ____________ then (𝒂𝒃)𝒙 = 𝒂𝒙 𝒃𝒙 .
The Rules can be deduced from the definitions. These five definitions and three rules are also
referred to as ‘ the laws of exponents’.
Why these Definitions are made and how these Rules are formed is a very interesting discussion!
But it isadvisable to have this discussion after starting using these facts thoroughly.