C1 - Algebra and Functions - Laws of Indices

In this First Post for C1. I shall be posting some notes and examples about the 1st topic in Algebra and Functions. This is about the laws of indices and surds.

Laws of Indices.
A variable raised to the power, is called an indice / index. We have certain rules we can apply, to simplify / manipulate, usually if the base of the power is the same.

1) x^a * x ^b = x^(a+b)   (X to the power of a multiplied by X to the power of b) = X to the power of (a+b)

2)x^a /  x^b = x^(a-b)   (X to the power of a divided by X to the power of b) = X to the power of (a-b)

3) (x^a)^b = x^(a*b) (X^a to the power of b) = X to the power of (a*b)

*** For the 3rd rule, the b will be adjacent to the a, I can't write it in the handwriting form. If there is a number in front of the x, this number will be raised to the power of b.

e.g. (3x^4)*2 = This means 3x to the power of 4 , the 2 is outside the bracket.

The answer would be 3 to the power of 2,multiplied by, x to the power of (4*2) =  (9x^8)

4) (x/m)^n = x^n / m^n (x divided by m, all the power of n = x to the power of n divided by m to the power of n).

General Facts

Anything to the power of 0 will be 1. I mean anything from a number to a variable.

Anythign to the power of 1 will be itself. e.g. 2^1 = 2 ,   (x^2) to the power of 1 = x^2

Other Rules
I have uploaded an image file explaining the rules, as it is not appropriate to write them up, as the typos can be hard to understand.

Handwritten Notes on Laws of Indices (Printable)

If any problem understanding the notes, or feedback email : mathematicsthesolver@gmail.com