Correct Answer - Option 2 : \({4^n}\)
\(\begin{array}{l}
\frac{{{\alpha ^n} + {\beta ^n}}}{{{\alpha ^{ - n}} + {\beta ^{ - n}}}} = \frac{{{\alpha ^n} + {\beta ^n}}}{{\frac{1}{{{\alpha ^n}}} + \frac{1}{{{\beta ^n}}}}}\\
= \frac{{\left( {{\alpha ^n}{\beta ^n}} \right)\left( {{\alpha ^n} + {\beta ^n}} \right)}}{{{\alpha ^n} + {\beta ^n}}}\\
= {\left( {\alpha \beta } \right)^n} = {4^n}
\end{array}\)