If $x = (0.25)^{\frac{1}{2}}, y = (0.5)^{2}, z = (0.216)^{\frac{1}{3}},$ then

$\frac{3}{4} \left(1+\frac{1}{3}\right) \left(1+\frac{2}{3}\right) \left(1-\frac{2}{5}\right) \left(1+\frac{6}{7}\right) \left(1-\frac{12}{13}\right)$ is equal to

If $P = \frac{(\sqrt{7} - \sqrt{6})}{(\sqrt{7} + \sqrt{6})},$ then what is the value of $\left(P + \frac{1}{P}\right)?$

If $2x + y = 17$,$y + 2z = 15$,and $x + y = 9$,then the value of $4x + 3y + z$ equals:

If $a+\frac{1}{a}+2=0,$ then the value of $\left(a^{37}-\frac{1}{a^{100}}\right)$ is

Simplify:
$\frac{a^{1 / 2}+a^{-1 / 2}}{1-a}+\frac{1-a^{-1 / 2}}{1+\sqrt{a}}$