1.3333.. does NOT equal 4/3!

[Tavrobel]

This is what 3/10 looks like on paper.

Thanks for the approximation and using the rules of significant figures.

Continuing on...

While we're on the subject of math, what does any number with an exponent of zero equal one instead of zero or that same number?

An exponent is really division/multiplication, except in this case, an exponent is a multiplied number multiplied many times. So 4² is 16 (4*4), or 6³ is 216 (6*6*6), or can be expressed as 6¹⁺¹⁺¹. Simply put, exponents represent how many times a number is multiplied by itself. Is it still not itself when it is alone?

Exponential numbers can be modified by adding and subtracting, a shortcut for signifying that a number can be multiplied that many number of times. There are such things as identities, numbers you use to keep a number that you have. For exponents, an identity is anything to the X¹ == X. Exponents already use to the first power as equalling itself. Addition uses N+0 == N, N*1=N, N¹ == N.

Let's take a number, a variable: (A)
It can equal anything besides zero.

Second variable: (n)
This is our exponent.

Aⁿ/Aⁿ, is the same as saying A^{n - n}, since we can manipulate exponents however we want.

What happens when we subtract any number from itself? We get zero, the additive identity. After all, A + 0 is still A. Applied to division, A^{n - n} is the same as A⁰. When you divide anything by itself, it equals one. Therefore, A⁰ == 1, as long as A != 0.

There's a multiplicative proof using algebra, but the divison proof is easier to remember, even if it does use more mathematical theory than the other.