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

Express $0.\overline{4}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

For each question,select the proper option from four options given,to make the statement true: $\sqrt{5^{2}+12^{2}}$ is a / an $\ldots \ldots$ number.

Find three rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$.

Find three different irrational numbers between the rational numbers $\frac{1}{3}$ and $\frac{7}{9}$.

Express $0.\overline{27}$ in the $\frac{p}{q}$ form.