# CLASS-7EXPONENTS

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  =  3  (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 = 6 (Here read as 6 to the power 5 )

It can be remembered that – if  ( x to the power zero ‘0’ ) x =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.

Example1)  625 = 5 X 5 X 5 X 5 = 5

2) 8960 = 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 7 X 7

= 2  X  7²