WHY X^0=1? SIMPLE EXPLANATION WITH PROOF.

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Hi I am your teacher for today's question. My name is Anish .Hope this answer would help you to understand this concept. We all know that anything raise power zero =1 but do you questioned yourself why..?  in the ending of this blog you will aware of why is it zero..so stay tuned. 

WHAT IS A POWER ?

A power of a number is defined as how much time a number should be multiplied to itself like if I say what is 6^3 ? It simply means that 6 should be multiplied by itself 3 times. More examples are

1. 2^2 = 2*2 = 4
2. 3^3 = 3*3*3 =27

Now back to our question...

lets us make a table of powers of 2 like,

2^1=2
2^2=2*2=4
2^3=2*2*2=8
2^4=2*2*2*2=16

AS SHOWN IN FIG :



Now do you notice something...

There is this beauty of math's known as Pattern Recognition  . There is a pattern.. do you see it .
Here when 2^4 is divided by 2 we get 2^3 . As shown is figure



Similar condition goes with 2^3 and 2^2 as 2^3/2=2^2 and 2^2/2=2^1 . Hence from this we have no objection to  conclude that if we divide 2^1 with 2 we get 2^0.  because it is logically possible and is verified 3 times before. Hence  from the figure


hence we have conclude 2^0=1 . But wait..... is it valid for every number..?  The answer for this question is yes .Weather you take 1,2,3,4,5,....  it is valid for every number  for example  


Thats it  for today . See you next time...

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