If ${2^x} = {4^y} = {8^z}$ and $xyz = 288,$ then ${1 \over {2x}} + {1 \over {4y}} + {1 \over {8z}} = $
$11/48$
$11/24$
$11/8$
$11/96$
If $a = \sqrt {(21)} - \sqrt {(20)} $ and $b = \sqrt {(18)} - \sqrt {(17),} $ then
If ${a^x} = {b^y} = {(ab)^{xy}},$ then $x + y = $
$\root 4 \of {(17 + 12\sqrt 2 )} = $
If ${a^x} = bc,{b^y} = ca,\,{c^z} = ab,$ then $xyz$=
The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is