Tags: #math #factorials #exponents #power #raise
To identify the various combinations of a number or letter, you need to know the number of items.
So if you’re dealing with a string like “ABC”, that’s three characters.
So you would say 3! factorial.
Which really means: 3*2*1 = 6.
And the reason we multiply backwards from 3 specifically is because there were three characters to begin with.
So we know there are six potential combinations:
But what if you have 10 items?
10*9*8*7*6*5*4*3*2*1 = 3,628,800
You can see that even with a small number of items, the number of possible combinations becomes very large.
An exponent is made up of two numbers: a “base” and a “power” (also referred to as an “exponent”, but I prefer “power” as it helps to distinguish the second number from the over-arching concept of exponents).
Typically the power is displayed as a superscript, but as that not always the easiest thing to type in different editors there is also a symbol to represent an exponent: ^.
3^4 = 3*3*3*3
Note: strictly speaking the small (superscript) number is the “exponent”, while the larger number is the “base”. The base multiplying itself a number times (specifically by whatever number the exponent is set to) will result in what’s called “raising to the power” (the “power” is the resulting number). – see https://en.wikipedia.org/wiki/Exponentiation