Exponents
When a number is multiplied by itself repeatedly, then the product is called a power of a number. The number itself is called the base and the number of times it is multiplied is called the index or exponent.
Example -1
In four times we doing multiplication of the same number three and it can be written as = 3 x 3 x 3 x 3 = 3⁴ (Here read as 3 to the power 4)
Example -2
In five times we doing multiplication of the same number six and it can be written as = 6 X 6 X 6 X 6 X 6 = 6⁵ (Here read as 6 to the power 5 )
It can be remembered that – if ( x to the power zero ‘0’ ) x⁰ =1
( x to the power one ‘1’ ) x¹ = x
Classification of numbers -A number is called an Even numbers, if it is a multiple of 2 and for your information 2 is a factor of every even number. For example 4, 8, 16, 20, 24, 26, 32 are even numbers.
A number is called an Odd number if it is not a multiple of 2 and in the other words, an odd number is not exactly divisible by 2.
For example – 1, 3, 5, 7, 9, 11, 13, 15, 17, 19………
A number will be called as Prime numbers or Prime if it has no other factors except 1 and itself, for example - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,…… are some prime numbers and 2 is the only prime number and it is the smallest prime number but 1 is not considered as Prime number.
A number will be called as a Composite Number if it is a product of two or more prime numbers. 4, 6, 8, 9and 10 are some composite numbers.
Two natural numbers are called Co-prime numbers if they do not have a common factor except 1. For example, 3 & 4; 15 & 17; and 11 & 14 are co-prime numbers.
The process of writing a number as a product of prime numbers is called Prime factorization. If the same factor is repeated in the process, it is more convenient to express the factorization in the exponential form.
Example- 1) 625 = 5 X 5 X 5 X 5 = 5⁴
2) 8960 = 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 7 X 7
= 2⁹ X 7²