If \( 3^x - 3^{x-1} = 18 \), then find the value of \( x^x \). যদি \( 3^x - 3^{x-1} = 18 \), তবে \( x^x \) এর মান নির্ণয় করো।

Find the simplest value of:

\( \frac{1}{\sqrt{2}+\sqrt{3}}\) + \(\frac{1}{\sqrt{3}+\sqrt{4}}\) + \(\frac{1}{\sqrt{4}+\sqrt{5}}\) + \(\frac{1}{\sqrt{5}+\sqrt{6}} \)

Find the value of:

\[ \sqrt{6+\sqrt{6+\sqrt{6+\cdots}}} \]

If \( x = 2 + \sqrt{3} \) and \( y = 2 - \sqrt{3} \), then the value of $ \frac{x^2 + y^2}{x^3 + y^3} $ is: