For each question,select the proper option from four options given,to make the statement true: $(5^{-2})^{3} = \ldots \ldots \ldots$

If $a = \frac{\sqrt{5}}{8}$ and $\frac{8}{a} = b \sqrt{5}$,then find the value of $b$.

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three decimal places.
$\frac{1}{\sqrt{3}+\sqrt{2}}$

If $\frac{5+3 \sqrt{3}}{7+4 \sqrt{3}}=a+b \sqrt{3},$ find the value of $a$ and $b$.

Find the value of the following expression correct to three decimal places,rationalizing the denominator if needed. Take $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$.
$\frac{4}{3 \sqrt{3}-2 \sqrt{2}} + \frac{3}{3 \sqrt{3}+2 \sqrt{2}}$

Rationalise the denominator in each of the following:
$\frac{18}{3 \sqrt{2}-2 \sqrt{3}}$