Rucete ✏ Mathematics In a Nutshell
Index
Indices indicate the number of times a number or letter has been multiplied by its own values.
Example of index
2³ = 2*2*2 = 8
(2³ = 2^3)
The laws of Indices | In a nutshell
-> x^m * x^n = x^(m+n)
-> x^m / x^n = x^(m-n)
-> (x^m)^n = a^m*n
-> x^0 = 1
Negative exponets
-> x^-m = 1/x^m
-> (x/y)^-m = (y/x)^m
Example
1. x^3 * x^5 = x^8
2. x^7 / x^2 = x^5
3. (x^3)^4 = x^12
4. 3^0 = 1
5. 2^-5 = 1/2^5 = 1/32
6. (1/2)^-2 = (2/1)^2 = 4
To Surb form | In a nutshell
-> x^1/m = ₘ√x
-> x^n/m = ₘ√xⁿ
Example
1. 4^1/2 = 2√4 = 2
2. 16^3/4 = 4√16³ = 8