## What is an Exponent?

### Exponents

The repeated addition of numbers can be written in short form (product form). Examples: Also, we can write the repeated multiplication of numbers in a short form known as exponential form.
For example, when 5 is multiplied by itself for two times, we write the product 5 × 5 in exponential form as 52 which is read as 5 raised to the power two.

Similarly, if we multiply 5 by itself for 6 times, the product 5 × 5 × 5 × 5 × 5 × 5 is written in exponential form as 56 which is read as 5 raised to the power 6.
In 56, the number 5 is called the base of 56 and 6 is called the exponent of the base.

In general, we write,
An exponential number as ba, where b is the base and a is the exponent.
The notation of writing the multiplication of a number by itself several times is called the exponential notation or power notation.

Thus, in general we find that :
If ‘a’ is a rational number then ‘n’ times the product of ‘a’ by itself is given as a × a × a × a ….. , n times and is denoted by an, where ‘a’ is called the base and n is called the exponent of an.

### Examples

1. Write the following statements as repeated multiplication and complete the table:

 S.No. Statements Repeated Multiplication Short form (i) 3 multiplied by 3 for 6 times 3 × 3 × 3 × 3 × 3 × 3 = 729 36 (ii) 2 multiplied by 2 for 3 times 2 × 2 × 2 23 (iii) 1 multiplied by 1 for 7 times 1 × 1 × 1 × 1 ×  1 × 1 × 1 17

2. Write the base and exponent of following numbers. And also write in expanded form:

 S.No. Numbers Base Exponent Expanded Form Value (i) 34 3 4 3 × 3 × 3 × 3 81 (ii) 25 2 5 2 × 2 × 2 × 2 × 2 32 (iii) 33 3 3 3 × 3 × 3 27 (iv) 22 2 2 2 × 2 4 (v) 17 1 7 1 × 1 × 1 × 1 × 1 × 1 × 1 1

### Exponents of Negative Integers

When the exponent of a negative integer is odd, the resultant is a negative number, and when the power of a negative number is even, the resultant is  a positive number.When the exponent of a negative integer is odd, the resultant is a negative number, and when the power of a negative number is even, the resultant is  a positive number.
or (a negative integer) an odd number = a negative integer.
(a negative integer) an even number  = a positive integer.

Examples:

Ex.1 Express 144 in the powers of prime factors.
Solution:
144 = 16 × 9 = 2 × 2 × 2 × 2 × 3 × 3
Here 2 is multiplied four times and 3 is multiplied 2 times to get 144.
∴  144 = 24 × 32

Ex.2 Which one is greater : 35 or 53 ?
Solution:
35 = 3 × 3 × 3 × 3 × 3 = 9 × 9 × 3
= 81 × 3 = 243
and 53 = 5 × 5 × 5 = 25 × 5 = 125
Clearly, 243 > 125
∴  35 > 53