Important Formulas - Surds and Indices - Tricks & Shortcuts

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)

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(a^m)

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