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What is an Exponent?

December 11, 2020 by Prasanna

What is an Exponent?

Exponents

The repeated addition of numbers can be written in short form (product form).
What is an Exponent 1Examples:
What is an Exponent 2
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.

Read More:

  • What are Laws of Exponents?
  • Review of Exponents
  • Surds

Examples

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

S.No.StatementsRepeated MultiplicationShort form
(i)3 multiplied by 3 for 6 times3 × 3 × 3 × 3 × 3 × 3 = 72936
(ii)2 multiplied by 2 for 3 times2 × 2 × 223
(iii)1 multiplied by 1 for 7 times1 × 1 × 1 × 1 ×  1 × 1 × 117

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

S.No.NumbersBaseExponentExpanded FormValue
(i)34343 × 3 × 3 × 381
(ii)25252 × 2 × 2 × 2 × 232
(iii)33333 × 3 × 327
(iv)22222 × 24
(v)17171 × 1 × 1 × 1 × 1 × 1 × 11

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

Maths

Filed Under: Mathematics Tagged With: Exponents, Exponents of Negative Integers, Maths, Pre Algebra

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