#exponent rules

f^a x f^b = f^a+b

f^a / f^b = f^a-b

(f^a)^b = f^ab

(fg)^a = f^a x g^a

(f/g)^a = f^a / g^a

f^-a = 1 / f^a

(1/2)^3 = (1/2)*(1/2)*(1/2) = 1/8 = 0.125

(1/2)^-3 = (2/1)*(2/1)*(2/1) = 8/1 = 8

2^0 = 1

-2^0 = -1

-4^2 = -16

(-4)^2 = 16

3^-0 = 1

(-2)^-2 = 1/(-2)^2 = 1/4 = 0.25

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)