I tried to understand exponentiation, but I can't understand that why any base raised to the power of 0 becomes 1.
As per Wikipedia the definition of b raise to power n is multiplications of base n times. Shouldn't it make more sense if we say a unit quantity is increased/decreased by base n times. If not then how would you explain anything raise to power 0 as 1 in layman/practical terms, like say counting bananas.
Addition: By increase decrease I mean multiplied and divided. And please help me understand not by math formulas, as I am trying to imagine it in real world scenarios.
Best Answer
NO, "the number $b$ multiplied by itself $n$ times" is the definition of $b^n$ if $n$ is a positive integer; for other $n$ we need a different definition.
First thing to note about definitions is we can make any definition that we want; the only question is is it useful. There's no mathematical problem with the definition $$b^n=17$$ for all $b$ and $n$, but it would make exponentiation sort of useless.
So. How do we want to define $b^0$? We note that if $n$ and $m$ are both positive integers then $$b^{n+m}=b^nb^m\quad(*).$$That's a useful thing, so we try to preserve it when we extend the definition to $n=0$. Think about it for a second; defining $b^0=1$ is the only way to get $(*)$ to work for $n\ge0$.
Similarly for why we define $b^{-n}=1/b^n$.