${a^{m{{\log }_a}n}} = $
${a^{mn}}$
${m^n}$
${n^m}$
None of these
$\sqrt {(3 + \sqrt 5 )} - \sqrt {(2 + \sqrt 3 )} = $
The rationalising factor of $2\sqrt 3 - \sqrt 7 $ is
If ${\left( {{2 \over 3}} \right)^{x + 2}} = {\left( {{3 \over 2}} \right)^{2 - 2x}},$then $x =$
The value of $\sqrt {[12 - \sqrt {(68 + 48\sqrt 2 )} ]} = $
${{3\sqrt 2 } \over {\sqrt 6 + \sqrt 3 }} - {{4\sqrt 3 } \over {\sqrt 6 + \sqrt 2 }} + {{\sqrt 6 } \over {\sqrt 3 + \sqrt 2 }} = $