While studying exponents, we've been taught,
,but I don't think many people ponder, why is this so? Why are things the way they are! Curiosity is an important aspect of learning, and in this post, I'll try to make things more clear about "Laws of Exponents".First, before we start, we need to understand, why
.
can be written as -> 
now, we know, 
so we can write this equation as, 
. Everything will make sense, after an example, let's say we have 
=> 
that can be written as => 
In a nutshell, what we basically do is, divide the number of Xs in the numerator by the number of Xs in the denominator, and that is why we can write
as 
, because the number of X remaining after solving, will be equal to the number of Xs in the numerator subtracted by the number of Xs in the denominator.Now, if this is clear, then you'd probably guessed by now, that why
if you haven't then I'll give you a hint. "Any number subtracted from itself is 0". That is, 
, now, x0 can be written as 
,,
=> 
Now, as we know, 
, you can figure that out by yourself that this whole term will become 1. I hope this clears up why x0=1.
Now, while we are on the topic, I'll also explain why xm*ym = (x*y)m,
Imagine, we have a given term, xm*ym, that can be written as, (x*x*...*xm times)*(y*y*...*ym times). Now by Commutative Property Of Multiplication, we can write this equation as (x*y)*(x*y)* ... *(x*y)m times, and that is how and why we can write this equation as, (x*y)m.
I hope this post was worth your time. If you think, this post was helpful and can help someone understand this concept better, please don't forget to share them!
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