Surds, any root of rational number which cannot be easily calculated is known as Surd.

Rules of Surds

1. ${\left(\sqrt[n]{a}\right)}^n=a$
2. ${\left(\sqrt[n]{a}\right)}^m=\sqrt[n]{a^m}$
3. $\sqrt[n]{ab}=\sqrt[n]{a}\times \sqrt[n]{b}$
4. $\sqrt[m]{\sqrt[n]{a}}=\sqrt[mn]{a}$
5. $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$
6. $\sqrt{a}\times \sqrt{b}\times \sqrt{c}=\sqrt{abc}$
 
Indices, Let a be a real number amd m is a positive integer, then $a\times a\times a..... m times= a^m$. This is read as 'a raise to power m'. Here,a is known as base and m is known as index.

Rules of Indices

1. $a^m\times a^n=a^{m+n}$
2. $a^m÷a^n=a^{m-n}$
3. $(a^m{)}^n=a^{mn}$
4. ${\left(ab\right)}^m=a^m\times b^m$
5. ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$
6. $a^0=1$

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