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.
- Conversion of numbers to standard form
- 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