Is $\sqrt{8+15}$ a rational number or an irrational number?

If $125^{x} = \frac{25}{5^{x}},$ then find the value of $x$.

Prove that $\left(\frac{x^{a}}{x^{b}}\right)^{a+b} \times \left(\frac{x^{b}}{x^{c}}\right)^{b+c} \times \left(\frac{x^{c}}{x^{a}}\right)^{c+a} = 1$.

State whether the following statement is true or false:
Every whole number is a rational number.

Find the values of $a$ and $b$ in each of the following:
$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+\frac{7}{11} \sqrt{5} b$

$\sqrt[4]{\sqrt[3]{2^{2}}}$ equals