Simplify $: \frac{(25)^{\frac{3}{2}} \times(243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}} \times(8)^{\frac{4}{3}}}$
In each of the following numbers rationalise the denominator
$\frac{1}{5+2 \sqrt{3}}$
Between two rational numbers
If $125^{x}=\frac{25}{5^{x}},$ then find the value of $x$.
Simplify the following:
$\frac{3}{\sqrt{8}}+\frac{1}{\sqrt{2}}$