Chapter 1.4.1 - Exponents
Exponent := the number of times Real Number is multiplied against itself. For example: 3 * 3 * 3 = 3 ^3.
The following rules don’t have much of an explanation as they are pretty self explanatory. Or so I hope.
Exponent Addition
3 ^m * 3 ^n = 3 ^ (m + n)
Exponent Subtraction
3 ^m / 3 ^n = 3 ^m * 1 / 3^n = 3 ^m * 3^-n = 3 ^ (m - n)
Exponent Multiplication
3 ^m * 3 ^m * 3 ^m * 3 ^m * ... = (3 ^m) ^n = 3 ^( m * n )
Exponent Division
3 ^m * 3 ^m ... / 3 ^m * 3 ^m * ... = (3 ^m) ^n / (3 ^m) ^-z = 3 ^m ( n - z )
Exponents Across Variables
(ab)^n = a^n * b^n = a * a * a ... * b * b *b ...
Examples
(a / b) ^-n = 1 / (a / b) ^n = ( 1 / ( a / b ) ) ^n = ( 1 / a / b ) ^n = ( b / a ) ^n
Rules
a ^0 = 1
a ^-n = 1/a
a ^m * a ^n = a ^ (m + n)
a ^m / a ^n = a ^ (m - n)
(a ^m) ^n = a ^ (m * n)
(ab) ^m = a ^m * b ^m