Simplify:
$(\frac{3}{5})^4 + (\frac{8}{5})^{-12} + (\frac{32}{5})^{6}$
Fill in the blanks so as to make each of the following statements true (Final answer only)
$\sqrt{1 \frac{25}{144}}=\ldots \ldots$
Express $0.5 \overline{7}$ in the form $\frac{P}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$
Rationalise the denominator of the following:
$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$
If $a=2+\sqrt{3},$ then find the value of $a-\frac{1}{a}$