An Introduction to Exponents

Exponents

How about calculating the distance between moon and earth? You will be surprised that the distance is even greater than lakhs. The actual distance between moon and earth is 3, 84,400 Km. But it is really difficult to remember such a bigger distance value.

So, what can we do? We can try to simplify this bigger value. Why not write 3,84,400 as 6202. 620* 620 = 3, 84,400.

Thus, the exponent of a number implies about the number of times to use the number in a multiplication.


What are Exponents?

A simple natural number when expressed in the form of power, then it is called an exponent or power or indices.

In other words, we can also say that exponents are expressed in the form of multiple of the simplest numbers. Thus, by the exponent, you can simplify or reduce a bigger number into a much smaller number.


Exponents Examples

For Example, 625 can be written as 252 or 25 * 25 = 625. Here, 25 is the base and 2 is the exponent. Exponents can also be termed as power. And thus you can also say 2 is both exponent and power.

Exponent is extremely useful in regular mathematics. When you have large digits, then it is not possible to remember them fully. And thus they are expressed in the form of exponents.

For Example, 5612161 is such a large number. You can simplify and write it as, 2369 * 2369 = 5612161.

You can also write it as, 23692 = 5612161.


Types of Exponents

There are several types of exponents on the basis of their power. Let’s have a look at some of the major types of exponents:

  1. Positive Exponent – These exponents are the ones which have positive numbers as their power. For Example, 49 = 72 is a positive exponent.

  2. Negative Exponent – These exponents are the ones which have negative numbers as their power. For Example, 8-2. This needs to be simplified.

Let’s understand how to simplify a negative exponent.

When you have the number 8-2.

You need to first add 1 in the numerator and convert the number in question into the denominator. For Example, 8-2 = -1/8 * 1/8 = 1/64.

Thus, 8-2 can also be written as 1/64.

  1. Zero Exponent – These exponents are the ones when you have 0 in the power. 0 is equal to 1 and thus you don’t need to perform any special operation here.

For Example, 90 is equal to 91. It can also be written as,

90 = 91 = 9.

  1. Rational Exponent – These exponents are the ones which have a rational number or fractions as the power. For Example, 101/2 is the example of a rational exponent.

101/2 can be called as 2 roots of 10.


Rule of Exponents

Following are the simple but extremely useful rules of exponents:

  • A0 = 1: As per this rule, the power of a natural number is 0, and then the result will be 1.

  • AmAn = Am+n: As per this rule, when there are two same natural nos., then the different powers can be added together.

  • Am/n = Am-n: As per this rule, when power is in the rational form, then the numerator and denominator can be subtracted and brought to simple terms.

  • (Am)n = Am.n: As per this rule, when there are brackets between two different powers then it can be multiplied and then solved accordingly.

The above rules will help in solving any of the mathematical equations.

For Example,

(52)3 = 52*3 = 56 = 5 * 5 * 5 * 5 * 5 * 5 = 15625

Let’s solve one more example,

Simplify, 642/22

= (64/2)2

= (32)2

= 1024

Relation between Positive and Negative Power

ax = 1/a-x

Where, a is the base. X is the power or exponent.

Let’s understand this with an example,

52 = 1/5-2


Solved Examples:

Example: Simplify 62 + 43 + 72 - 23

Solution:

= 6 * 6 + 4 * 4 * 4 + 7 * 7 – 2 * 2 * 2

= 36 + 64 + 49 – 8

= 149 – 8

= 141

 

Example: Solve 16/22 + 32/42

Solution:

= 16/2*2 + 32/4*4

= 16/4 + 32/16

= 4 + 2

= 6


Example: Solve 102 * 103 + 25

Solution:

= 100 * 1000 + 32

= 100000 + 32

= 100032


Example: Solve 172 * 183

Solution:

= 289 * 5832

= 1685448


Fun Facts

  • Exponents, on contrary to multiplication, do NOT "distribute" over addition.

  • Anything raised to the power zero (0) is just "1" (until and unless "anything" is not itself zero).

FAQs (Frequently Asked Questions)

Q1. What do You Understand by Power or Exponents?

Answer: You have already been given an introduction to exponents or know what exponents are. Exponent is the representation of a bigger number into a simpler and smaller number.


For Example, when 25 is written as 52. Then 25 is the bigger number which is expressed as 52. Here 5 is the base and 2 is the power or exponent.

Q2. What will be the Solution, When the Exponent is 0 or 1?

Answer: If the exponent is 1 of a base number, then the answer will be the base number only.

For Example,  111 = 11.

And when the exponent is 0 of the base number, then the resultant will be 1.

For Example, 70 = 1.

Q3. What is Included in CBSE Class 11 Maths Revision Notes Chapter 8  - An Introduction to Exponents.

Answer: CBSE Class 11 maths chapter 8 notes PDF free download is a crucial part of CBSE Chapter 8 introduction to exponents for quick revision and last minute best preparation. Here, you will find the NCERT notes on introduction to exponents for Class 11 Maths designed by experts at Vedantu keeping in consideration the updated pattern and guidelines by the CBSE Board.