IMPORTANT FACTS AND FORMULAE OF SURDS AND INDICES

1. LAWS OF INDICES:

 

(i)                 a^m x aⁿ = a^{m + n}

(ii)    a^m_­ / aⁿ = a^m-n

(iii)             (a^m)ⁿ = a^mn

(iv)             (ab)ⁿ = aⁿbⁿ

(v)     ( a/ b )ⁿ = ( aⁿ / bⁿ )

(vi)             a⁰ = 1

 

                                                                                                        

2. SURDS: Let a be a rational number and n be a positive integer such that a^1/n = ⁿsqrt(a)

   is irrational. Then ⁿsqrt(a)  is called a surd of order n.

 

3. LAWS OF SURDS:

 

(i)  ⁿ√a = a^1/2

(ii) ⁿ √ab = ⁿ √a * ⁿ √b

(iii) ⁿ √a/b = ⁿ √a  /  ⁿ √b

(iv) (ⁿ √a)ⁿ = a

(v) ^m√(ⁿ√(a)) = ^mn√(a)

(vi) (ⁿ√a)^m = ⁿ√a^m