Represent $\sqrt{9.3}$ on the number line.

Rationalize the denominators of the following:

(i) $\dfrac{1}{\sqrt{7}}$

(ii) $\dfrac{1}{\sqrt{7} - \sqrt{6} }$

(iii)$\dfrac{1}{\sqrt{5} + \sqrt{2} }$

(iv)$\dfrac{1}{\sqrt{7} - 2 }$

Find:

(i) $\left(9^{\smash{\frac{3}{2}}} \right)$

(ii) $\left(32^{\smash{\frac{2}{5}}} \right)$

(iii) $\left(16^{\smash{\frac{3}{4}}} \right)$

(iv) $\left(125^{\smash{\frac{-1}{3}}} \right)$

Simplify:

(i) $\left(2^{\smash{\frac{2}{3}}} \right)$. $\left(2^{\smash{\frac{1}{5}}} \right)$

(ii) $\Big(\dfrac{1}{3^3}\Big)^7$

(iii) $\dfrac{11^\frac{1}{2}}{11^\frac{1}{4}}$

(iv) $\left(7^{\smash{\frac{1}{2}}} \right)$. $\left(8^{\smash{\frac{1}{2}}} \right)$