In mathematics, an index (or power) is a small number written to the right and above a base number, which tells how many times the base number should be multiplied by itself. The plural of index is indices. In algebra, indices are used to represent numbers in a compressed form, and they are also used to simplify calculations or expressions involving powers of the same base. There are several laws of indices, including multiplying, dividing, power of 0, brackets, negative and fractional powers, which are necessary to understand before dealing with indices. Some important rules of index numbers include:
- ya × yb = ya+b
- ya ÷ yb= ya-b
- y -b = 1/yb
- ym/n = (n√y)m
- (yn)m = ynm
- y0 = 1
Indices can be positive or negative numbers, and they are used in various mathematical fields, including algebra, calculus, and physics.
