Categories
Mathematics

Basic Concept of Laws of Indices

A number of the form am where a is a real number, a is multiplied by itself m times

The number a is called the base and the super script m is called the index (plural indices) or exponent.

  1. m x A n = Am + n ——————–Multiplication law

Example:  XxX =( X x Xx X) x (X x X) = X 5

Or X3 x X2 = X3 + 2 = X5

  1. Am ÷ An=Am-n  ———————Division law

Example: X6 ÷ X= X6-4 = X2

  1. (a )= amn —————-Power law

Example:  (x3)2 = X3 x X3 = X3+3 =X6

Or X3X2 = X6

  1. am ÷ am = am-m = a=1

a÷am = am/am = ao = 1

a0………………………………….Zero Index

:. Any number raised to power zero is 1

Example: 3o = 1, co = 1, yo = 1

  1. (ab)m =amb  ————-Product power law

e.g. (2xy)2= 4x2y2

  1. Negative index

–m = 1/am        ————- Negative Index

Example: 2 -1 = ½, and 3 -2 = 1/3 2 = 1/9

  1. a1/n =n√a  ————–Root power law

Example : 9 ½ =√9=3

27 1/3 =3√27 = 3 ie (3)= 3

  1. m/n = (a 1/nm = (n√a)m ———–Fraction Index

or a m/n = (am1/n =   (n√a)m

Example : 272/3 = 3√27=32=9.

EVALUATION

  1. 275/3 2.   10000000000

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