Simplify:

$(\frac{3}{5})^4 + (\frac{8}{5})^{-12} + (\frac{32}{5})^{6}$

The value of $1.999 ....$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0,$ is

Express $0 . \overline{83}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$.

For each question, select the proper option from four options given, to make the statement true : (Final answer only)

$\left(5^{\frac{3}{4}}\right)^{\frac{4}{3}}=\ldots \ldots \ldots$

If $x=5+2 \sqrt{6},$ then find the value of $x^{2}+\frac{1}{x^{2}}$ and $x^{3}+\frac{1}{x^{3}}$

If $\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{6}}=a+b \sqrt{30},$ find the value of $a$ and $b$.