Tips in Maths-Indices

Indices are numbers with powers. The analysis and simplification depend on the basic interpretation and rules of indices as shown below

Basic Interpretation

i. Number with zero power: This is taken as 1 i.e a¤= 1. 20¤= 1
ii. Number with a negative power:

This is taken as the reciprocal of the result remaining when the negative sign is removed.

e.g a superscript -1 = 1/asup1 = 1/a 2 sup-3 = 1/2sup3 =1/2x2x2= 1/8.
Also, 1/8 can be taken as 1/8sup1 =8 sup 1 (as 1 means negative) and 1/8 can be taken as 1/2sup3 = 2sup-3

iii. Number with fractional powers: This is simplified by taking the denominator of the fraction as the root and the numerator as the power of the result remaining.
e.g asupb/c = (square c/a)b.

Laws of Indices

i. Product of numbers with the same base : This is done by taking one of the bases and summing their powers e.g asupb x asupc = asupb+c
Also asupb+c can be broken as asupa x asupc.

iii. Division of numbers with the same base : This is done by taking one of the bases and subtracting their powers e.g
asupb/ asupc or asupb/asupc= asupb-c

questions on Indices

Example 1.
The value of 16sup1/8 is A. 4 B. 2 C. 2squared D. 2 root 2 Tip (2sup4) = 2sup1/2 = 2square Ans D.