Indices & Surds - Teach.sg

Laws of Indices

$a^m \times a^n = a^{m+n}$

$a^m \div a^n = a^{m-n}$

$(a^m)^n = a^{mn}$

$a^0 = 1$

$a^{-n} = \dfrac{1}{a^n}$

$a^{\frac{1}{n}} = \sqrt[n]{a}$

$a^{\frac{m}{n}} = (\sqrt[n]{a})^m$

$(ab)^n = a^n b^n$

$\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}$

$\sqrt{a} \times \sqrt{a} = a$

$\sqrt{a} \times \sqrt{b} = \sqrt{ab}$

$\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\dfrac{a}{b}}$

$m\sqrt{a} + n\sqrt{a} = (m+n)\sqrt{a}$

$m\sqrt{a} - n\sqrt{a} = (m-n)\sqrt{a}$

Single surd

For $\dfrac{k}{a\sqrt{b}}$, multiply by $\sqrt{b}$.

Two surds

For $\dfrac{k}{a\sqrt{b}+c\sqrt{d}}$, multiply by conjugate $a\sqrt{b}-c\sqrt{d}$.