Laws of Indices

If we multiply a number with this number, indices will be formed. Suppose 5x5x5=125=5³. Here we can call 5 as base and 3 as index. The index of a number shows how many times a base number  has been multiplied by itself. Index is also called Power. It is also known as Exponent. The plural of index is indices.

The main reason we use exponents is because it's a shorter way to write out big numbers. For example, let's say we want to express the following:

2×2×2×2×2×2 

we can see that 2 is multiplied by itself 6 times. This means we can write the same thing with 2 as the base and 6 as the exponent. That is 2⁶.

Law of Indices:  

To manipulate expressions involving indices we use rules known as the laws  of  indices.
When m and n are two positive integers --

1. a^m × aⁿ = a^{m + n}

2. a^m ÷ aⁿ = a^{m - n} (m ≥ n)

3. (a^m)ⁿ = a^{m × n}

4. a⁰= 1

5. a^-m= 1/a^m

Some extra rules:

6. (a × b)ⁿ = aⁿ × bⁿ 

7. (a/b)ⁿ = aⁿ ÷ bⁿ

8. (a)^1/n = ⁿ√a 

 
Last revised: 17/08/2016