INDICES

INDICES AND THE LAW OF INDICES

Introduction

Indices are a useful way of more simply expressing large numbers. They also present us with many useful properties for manipulating them using what are called the Law of Indices.

What are Indices?

The expression a⁵ is defined as follows:

a^{5 =}  a x a x a x a x a

We call "a" the base and "5" the index.

Law of Indices

To manipulate expressions, we can consider using the Law of Indices. These laws only apply to expressions with the same base, for example, 3⁴ and 3² can be manipulated using the Law of Indices, but we cannot use the Law of Indices to manipulate the expressions 3⁵ and 5⁷ as their base differs (their bases are 3 and 5, respectively).

And This is my 6 rules of the Law Of Indices

1. 

 An Example :

Simplify 2^{0 :}

2.

An Example :

Simplify 2^-2:

3.

An Example :Simplify 5 x 5^3: (note 5 = 5¹)

4.

An Example :

Simplify  

5.

An Example :

Simplify (y²)⁶ :

6.

An Example :

Simplify 125^2/3:

References:

http://mathematics.laerd.com/maths/indices-intro.php

https://www.youtube.com/watch?v=LrvKAMgcipo

https://www.youtube.com/watch?v=SCnADV1pgXU