Indices

Indices Diagram

What is Indices? 

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?

6² (6 to the power of 2) is called ‘6 squared’

8³ (8 to the power of 3) is called ‘8 cubed’ 

You can write 5 * 5 * 5 * 5 as 5⁴

You say ‘5 raised to the power of 4⁵, or ‘5 to the power of

4⁵. The 4 is called the index.

Example: 

^{Laws of Indices}

   

Examples & Exercise:

Calculate the following :-

(a) 2⁰ + 2¹ + 3⁰ = 1 + 2 + 1 = 4

(b) 2³ * 2⁴ / 2⁶ = 2³⁺⁴ / 2⁶ = 2⁷ / 2⁶ = 2¹

(c) 16^-2 = 1 / 6² = 1 / 256

(d) 16^-1/2 = 1 / 16^1/2 =   = 1 / 16 = ¼

(e) (2³)² = 2⁶

(f) 25^3/2 = and then use cube root of 25 = 5³ = 125

Tips how to use the every these 6 laws: 

Law 1 : Any number whose to the power root of 0 is = 1, except 0.

Nevertheless of the value base.

Law 2 : On the formula it says multiply but you had to invert it become sign plus.

Law 3 : So likewise this rule, you had to convert it become minus. 

Law 4 : Any number whose to the power root of any negative number, you have to convert into this value = 16^-2 = 1 / 6²

Law 5 : Using this formula for example this question simplify

125^-2/3,  so you have to know which one is a & m, once you know you have to arrange it and then recognised the cube root of 125 is 5 so that it easy to know the value.

  

Law 6 : To raise an expression to the nth index, copy the base and times the power root.