# Surd and Indices

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Law of indices
1. $a^ma^n = a^{m+n}$
2. $\frac{a^m}{a^n} =a^{(m-n)}$
3. ${(a^m )}^n = a^{mn}$
4. ${(ab)}^n = a^n* b^n$
5. $(\frac{a}{b})^n = \frac{a^n}{b^n}$
6. $a^0 = 1$

laws of surds

1. $\sqrt[n]{a}= a^{\frac{1}{n}}$
2. $\sqrt[n]{ab}= \sqrt[n]{a} * \sqrt[n]{b}$
3. $\sqrt[n]{\frac{a}{b}}= \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$
4. $\sqrt[n]{a}^n = a$
5. $\sqrt[m]{\sqrt[n]{a}} ={\sqrt[mn]{a}}$
6. $(\sqrt[n]{a})^m = \sqrt[n]{a^m}$