Indices and Its Various Laws

Indices is a measure of the price performance of a group of stocks on an exchange. Trading indices allows you to access the entire economy or industry at once, and only need to open a position. Indices are a useful way to express large numbers more simply. They also provide us with many useful properties for manipulating them using the so-called Law of Indices.

 

  1. Conversion of numbers to standard form
  2. Law of indices, indicial equation

 

Example:       1       = 27(1 – x)

                       81(x – 2)

 

 

 

Solution:

   1     = 27(1 – x)

81(x – 2)

     1     = 33(1 – x)

34(x – 2)

3-4(x – 2) = 33(1 – x)

-4(x – 2) = 3(1 – x)

-4x + 8 = 3 – 3x

4x – 3x = 8 – 3

x = 5

 

            Example 2:

            6253/8 x 51/2   25

6253/8 x 51/2

52

53/2 x 51/2  = 53/2 + ½

52               52

= 54/2 => 52 => 52-2 = 50 => 1

52        52

 

 

 

i. Multiplication rule

Xa x Xb = Xa+b

 

ii. Division rule

Xa /  Xb = Xa-b

 

iii. Zero Index

XO = 1, X 0

 

iv. Power law:- (ax)y = axy

E.g. (23)2 = 23 x 23

= 2 x 2 x 2 x 2 x 2 x 2 = 26

(23)2 = 23×2 = 26

 

v. Product power law:- (ab)x = axbx

E.g. (3pq)2 = 32 x p2 x q2

= 9p2q2

 

vi. Negative Index

e.g.      26  . 29 = 26 = 2 x 2 x 2 x 2 x 2 x 2

29    2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 1/23

 

 

Also 26  29 = 2-3

2-3 = 1/23

 

 

 

  • Roof Power e.g.

91/2 = 9 = 3

 

 

 

  • Fraction Index

e.g. (i)  45/2 = ()5 = 25 = 32

(ii) 84/3 = ()4 = 24 = 16

 

 

e.g. 3.5682

Integer    decimal fraction

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