The value of $\sqrt {[12 - \sqrt {(68 + 48\sqrt 2 )} ]} = $
$2 + \sqrt 2 $
$2 - \sqrt 2 $
$\sqrt 2 - 1$
None of these
The value of the fifth root of $10^{10^{10}}$ is
${a^{m{{\log }_a}n}} = $
If ${a^x} = {b^y} = {(ab)^{xy}},$ then $x + y = $
${({x^5})^{1/3}}{(16{x^3})^{2/3}}$${\left( {{1 \over 4}{x^{4/9}}} \right)^{ - 3/2}} = $
If ${2^x} = {4^y} = {8^z}$ and $xyz = 288,$ then ${1 \over {2x}} + {1 \over {4y}} + {1 \over {8z}} = $