Surds and Indices

Laws of Indices

a) a^m + aⁿ = a^{m + n}

b) a^m ÷ aⁿ = a^{m - n}

c) (a^m)ⁿ = a^mn

d) (abⁿ) = aⁿbⁿ

e) (a/b)ⁿ = (aⁿ/bⁿ)

f) a⁰ = 1

Surds

Let a be a rational number and n be a positive integer such that a^(1/n) = ⁿ$\sqrt{a}$

Then ⁿ$\sqrt{a}$ is called a surd of order n

Laws of Surds

a) ⁿ$\sqrt{a}$ = a^(1/n)

b) ⁿ$\sqrt{ab}$ = ⁿ$\sqrt{a}$ x ⁿ$\sqrt{b}$

c) ⁿ$\sqrt{a/b}=$ⁿ$\sqrt{a}$/ⁿ$\sqrt{b}$

d) (ⁿ$\sqrt{a}$)ⁿ = a

e) (ⁿ$\sqrt{a}$)^m = ⁿ$\sqrt{a}$^m