(a)[1]
Write $500$ as the product of its prime factors.
(b)[3]
With $M = 2 \times 3^2$ and $N = 2^4 \times 3^2$, determine the values of $p$ and $q$ in each part: (i) $M \times N = 2^p \times 3^q$, (ii) $M \div N = 2^p \times 3^q$, (iii) $N^2 = 2^p \times 3^q$.