Gaurav Bole

why is x^0 = 1?

As we all know

• 2^1 = 2
• 2^2 = 4
• 2^3 = 8
• 2^4 = 16
• 2^5 = 32

….. and so on

as we increase the power of 2 the result value increases, but what if we go in the reverse direction let's check now,

2^5 = 32        2^4 = 16

    32/2 = 16 = 2^4

hear we divide result value with 2 then we will get previous power value values.

2^4 = 16        2^3 = 8

     16/2 = 8 = 2^3      


2^3 = 8      2^2 = 4

     8/2 = 4 = 2^2   


2^2 = 4         2^1 = 2 

     4/2 = 2 = 2^2

And Now,

2^1 = 2      2^0 = 1

     2/2 = 1 = 2^0

we can also check negative powers

2^0 = 1     2^-1 = ½

      ½ = ½ = 2^-1

Now, 0! = 1

1 ! = 1 2 ! = 2 3 ! = 6 4 ! = 24

and so on, now we go backward

24 / 4 = 6 (we got the previous value which is 3 ! )

6 / 3 = 2

2 / 2 = 1

and now 1 / 1 = 1 = 0 !