Number of Solution of the equation ${(x)^{x\sqrt x }} = {(x\sqrt x )^x}$ are

Solution of the equation  ${4.9^{x - 1}} = 3\sqrt {({2^{2x + 1}})} $ has the solution

If ${a^x} = {(x + y + z)^y},{a^y} = {(x + y + z)^z}$, ${a^z} = {(x + y + z)^x},$ then

${{3\sqrt 2 } \over {\sqrt 6 + \sqrt 3 }} - {{4\sqrt 3 } \over {\sqrt 6 + \sqrt 2 }} + {{\sqrt 6 } \over {\sqrt 3 + \sqrt 2 }} = $

The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is

${{\sqrt {(5/2)} + \sqrt {(7 - 3\sqrt 5 )} } \over {\sqrt {(7/2)} + \sqrt {(16 - 5\sqrt 7 )} }}=$