Indices

Introduction

Indices is more useful in simply expressing large number and show us many useful thing to manipulating them using what are called the Law of indices. 

The expression 2⁵ is defined as follows:

They call "2" the base and "5" the index.

Law of Indices

To manipulate expressions, by 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 can't use the Law of Indices to manipulate the expressions of 3⁵ and 5⁷ as their base differs (their bases are 3 and 5, respectively). 

There are 6 rules for this Law of Indices 

first: 

Any number, except 0, whose index is 0 is always equal to 1, regardless of the value of the base.

An Example:

Simplify 2⁰:

Second:

An Example:

Simplify 2^-2:

Third: 

To multiply expressions with the same base, copy the base and add the indices.

An Example:

Simplify : (note: 5 = 5¹)

Fourth: 

To divide expressions with the same base, copy the base and subtract the indices.

An Example:

Simplify

:

Fifth: 

To raise an expression to the nth index, copy the base and multiply the indices.

An Example:

Simplify (y²)⁶:

Sixth:

An Example:

Simplify 125^2/3:

Here's the video for more detail and easy to understand because in this it shows how the indices be solve.

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

https://www.youtube.com/watch?v=AB3ARY9V0Cw