The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is
${a^{1/3}} - {a^{ - 1/3}}$
${a^{2/3}} + {a^{ - 2/3}}$
${a^{2/3}} - {a^{ - 2/3}}$
${a^{2/3}} + {a^{ - 2/3}} - 1$
If ${({a^m})^n} = {a^{{m^n}}}$, then the value of $'m'$ in terms of $'n'$ is
${{{{[4 + \sqrt {(15)} ]}^{3/2}} + {{[4 - \sqrt {(15)} ]}^{3/2}}} \over {{{[6 + \sqrt {(35)} ]}^{3/2}} - {{[6 - \sqrt {(35)} ]}^{3/2}}}} = $
Number of value/s of $x$ satisfy given eqution ${5^{x - 1}} + 5.{(0.2)^{x - 2}} = 26$.
Let ${7 \over {{2^{1/2}} + {2^{1/4}} + 1}}$$ = A + B{.2^{1/4}} + C{.2^{1/2}} + D{.2^{3/4}}$, then $A+B+C+D= . . .$
Solution of the equation $\sqrt {(x + 10)} + \sqrt {(x - 2)} = 6$ are