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Surd and Indices

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}

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