If $2^{x-2} \cdot 3^{2 x-6}=36,$ then find $x$.

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

Simplify the following:

$4 \sqrt{28} \div 3 \sqrt{7}$

Simplify

$7^{\frac{1}{4}} \cdot 12^{\frac{1}{4}}$

Rationalise the denominator of the following:

$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Rationalise the denominator of the following:

$\frac{16}{\sqrt{41}-5}$