If $x+\frac{1}{x}=2,$ then the value of $x^{100}+\frac{1}{x^{100}}$ is

If $\frac{1}{\sqrt{a}} - \frac{1}{\sqrt{b}} = 0$,then the value of $\frac{1}{a} + \frac{1}{b}$ is

What is the value of $5 \frac{1}{2} + 7 \frac{1}{2} + 11 \frac{1}{2}$?

What mathematical operation should come at the place of $?$ in the equation $2 ? 6 - 12 \div 4 + 2 = 11$?

Simplify $\left(\frac{1}{64}\right)^{0}+(64)^{-1 / 2}+(-32)^{4 / 5}$

If $M = \left(\frac{3}{7}\right) \div \left(\frac{6}{5}\right) \times \left(\frac{2}{3}\right) + \left(\frac{1}{5}\right) \times \left(\frac{3}{2}\right)$ and $N = \left(\frac{2}{5}\right) \times \left(\frac{5}{6}\right) \div \left(\frac{1}{3}\right) + \left(\frac{3}{5}\right) \times \left(\frac{2}{3}\right) \div \left(\frac{3}{5}\right)$,then what is the value of $\frac{M}{N}$?