Find the value

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

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.

Multiply $5 \sqrt{3}$ and $4 \sqrt{12}$.

Fill in the blanks so as to make each of the following statements true (Final answer only)

$(64)^{-\frac{1}{6}}=\ldots \ldots$

Represent geometrically numbers on the number line:

$\sqrt{8.1}$

Simplify

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