Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.1\overline{34}$

Rationalise the denominator of the following: $\frac{\sqrt{40}}{\sqrt{3}}$

State whether the following statements are true or false. Justify your answer.
$(i)$ The square of an irrational number is always rational.
$(ii)$ $\frac{\sqrt{12}}{\sqrt{3}}$ is not a rational number as $\sqrt{12}$ and $\sqrt{3}$ are not integers.

$\sqrt{10} \times \sqrt{15}$ is equal to

Simplify $\left(4^{\frac{1}{5}}\right)^{3}$.

Simplify: $\frac{11^{\frac{1}{3}}}{11^{\frac{1}{5}}}$