Why any number power 0=1?

In order to increase a number to the nth power, we must first multiply it by itself n times. For instance, $2^2=2\cdot <!--\; \cdot \; -->2=4,2^3=2\cdot <!--\; \cdot \; -->2\cdot <!--\; \cdot \; -->2=8,3^4=3\cdot <!--\; \cdot \; -->3\cdot <!--\; \cdot \; -->3\cdot <!--\; \cdot \; -->3=81$, and so on. Therefore, when we multiply a number by itself zero times, we are actually not multiplying anything at all. This is known as raising a number to the zeroth power. Why does that matter? Well, let's go even farther back to the simplest case: addition. What happens when we add no numbers at all? Well, since we aren't adding anything, we should anticipate receiving zero. However, zero is also a very unique number. It is known as the additive identity because it is the only number that can be added to any other number without changing it. In other words, for any number x, 0 is the only number such that, $x+0=x$. Therefore, if adding no numbers at all results in the additive identity, it makes obvious that multiplying no numbers at all should result in the multiplicative identity. Now, what's the multiplicative identity? Well, it's the only number which can be multiplied by any other number without changing that other number. In short, the multiplicative identity is the number 1, because for any other number x, $1\cdot <!--\; \cdot \; -->x=x$. Because any number to the power of zero is just the result of no other numbers at all, or the multiplicative identity, 1, any number to the power of zero must be one.