Find the value

$\left(\frac{1}{27}\right)^{-\frac{2}{3}}$

Insert a rational number and an irrational number between the following:

$2.357$ and $3.121$

Simplify the following:

$\frac{2 \sqrt{3}}{3}-\frac{\sqrt{3}}{6}$

Simplify:

$64^{-\frac{1}{3}} + 64^{\frac{1}{3}} - 64^{\frac{2}{3}}$

Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:

$(i)$ $x^{2}=5$

$(ii)$ $\quad y^{2}=9$

$(iii)$ $z^{2}=.04$

$(iv)$ $u^{2}=\frac{17}{4}$

Simplify

$3^{\frac{2}{3}} \cdot 3^{\frac{4}{3}}$