Simplify:

$\frac{9^{\frac{1}{3}} \times 27^{-\frac{1}{2}}}{3^{\frac{1}{6}} \times 3^{-\frac{2}{3}}}$

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

If $\sqrt{5}=2.236,$ then evaluate $\frac{4-\sqrt{5}}{\sqrt{5}}$ correct to four decimal places.

Simplify: ${(256)^4}^{-\frac{3}{2}}$

Find the value of $a$ :

$\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a-6 \sqrt{3}$

Rationalise the denominator of the following:

$\frac{3+\sqrt{2}}{4 \sqrt{2}}$