Unit-10 | Indices | Class-10
Overview: Indices (sing. Index) is the exponent of any base. Index or exponent is the number that shows how much the base is raised to the power of. There are some laws of indices that come really handy when solving the algebraic expressions.
Contents
Indices
Laws of Indices
Indices:
In an algebraic term, we can have base, coefficient and the power. The power of a base in an expression is called its index. The plural form of index is indices.
In algebra, Indices is the representation of the power of the base of an algebraic term.
For example:
We have,
a*a . We write a*a as a². This '2' written as the exponent after a represents the base 'a' is raised to the power of '2'.
Laws of Indices:
There are some laws of indices that come really handy when solving expressions. This laws are the proven rules that can be applied to solve any algebraic expressions.
Here are some of the laws of indices according to different conditions:
| Laws | Expressions |
|---|---|
| Multiplication Law | a^m x a^n = a^(m+n) |
| Division Law | am + an = am-n |
| Power law of Indices | (am)n = am x n (ab)m = am x bm (a + b)m = am + bm |
| Law of Negative Powers | a-m = $\frac{1}{am}$ a^m = 1/ a^(-m) |
| Law of Zero Powers | a0 = 1 20 = 1 |
| Root law of Powers | m√ (am) = a^(m+n) |
0 Comments