Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :

$0.404040 \ldots$

The decimal expansion of the number $\sqrt{2}$ is

Is $\sqrt{8^{2}+15^{2}}$ a rational number or an irrational number ?

Find the value of $\frac{4}{(216)^{-\frac{2}{3}}}+\frac{1}{(256)^{-\frac{3}{4}}}+\frac{2}{(243)^{-\frac{1}{5}}}$

Find the value

$\frac{8 \frac{1}{3} \times 16 \frac{1}{3}}{32^{-\frac{1}{3}}}$

Simplify $: \frac{(25)^{\frac{3}{2}} \times(243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}} \times(8)^{\frac{4}{3}}}$