Important Formulas - Surds and Indices - Tricks & Shortcuts

1. Laws of Indices:
i. am x an = am + n
ii. am/ an =  am - n
iii. (am)n = amn
iv. (ab)n = anbn
v.  (a/b)n = (an )/(bn)

2. Surds:
Let a be rational number and n be a positive integer such that a(1/n) = nth root of a
Then, is called a surd of order n.

3. Laws of Surds:
i.  nth root of a = a(1/n)

ii. nth root of ab = nth root of a * nth root of b
iii. nth root of (a/b) = (nth root of a)/ (nth root of b)
iv.  (nth root of a)n=a
v. mth root of(nth root of a)) = mnth root of a
vi. (nth root of a)m = nth root of(am)


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