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

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

For $x \ne 0,{\left( {{{{x^l}} \over {{x^m}}}} \right)^{({l^2} + lm + {m^2})}}$${\left( {{{{x^m}} \over {{x^n}}}} \right)^{({m^2} + nm + {n^2})}}{\left( {{{{x^n}} \over {{x^l}}}} \right)^{({n^2} + nl + {l^2})}}=$

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

If ${({a^m})^n} = {a^{{m^n}}}$, then the value of $'m'$ in terms of $'n'$ is

Solution of the equation $\sqrt {(x + 10)} + \sqrt {(x - 2)} = 6$ are