Paper 2 · Calculator

Express $504$ as a product of its prime factors in index form.

The integer $504k$ is a perfect square, where $k$ is a positive integer. Find the smallest possible value of $k$.

Simplify completely $\frac{\sqrt{504}}{\sqrt{14}}$, giving your answer as an integer.

Express $\frac{6}{\sqrt{7} - 1}$ in the form $a + \sqrt{b}$, where $a$ and $b$ are integers.