Law of indices :
1 ) \[a^{m } \times a^{n} = a^{m+n} \]
2) \[\frac{a^{m } }{a^{n}} = a^{m-n} \]
3) \[\left ( a^{m} \right )^{n}= a^{mn} \]
4) \[\left ( ab \right )^{n}= a^{n}b^{n} \]
5) \[\left ( \frac{a}{b} \right )^{n}=\frac{ a^{n}}{b^{n}} \]
6) \[a^{0}=1 \]
Surds : Let a be a rational number and n be a positive integer such that \[a^{\frac{1}{n}}=\sqrt[n]{a} \] is irrational. Then, \[\sqrt[n]{a} \] is called a surd of order n.
Laws of surds :
1) \[\sqrt[n]{a} = a^{\frac{1}{n}} \]
2) \[\sqrt[n]{ab} = \sqrt[n]{a} \times \sqrt[n]{b} \]
3) \[\sqrt[n]{\frac{a}{b}} =\frac{ \sqrt[n]{a}}{\sqrt[n]{b}} \]
4) \[\left ( \sqrt[n]{a} \right )^{n} = a\]
5) \[\sqrt[m]{\sqrt[n]{a}} = \sqrt[mn]{a} \]
4) \[\left ( \sqrt[n]{a} \right )^{m} = \sqrt[n]{a^{m}} \]
Note : Use ^ symbol for power operations and $ symbol for root operations.
Example : 1) To find a to the power of n i.e \[a^{n} \] input : a^n.
2) To find a surd of order n i.e \[\sqrt[n]{a} \] input : a$n
3) \[\sqrt[4]{\sqrt[2]{12}} \] type this expression in input as ((12)$2)$4
4) \[\left [ 5\left ( 8^{\frac{1}{3}} +27^{\frac{1}{3}}\right ) ^{3}\right ]^{\frac{1}{4}} \] type this expression in input field as [5*(8^(1/2)+27^(1/3))^3]^(1/4)
