Given f(n)=O(n$^{2}$) and g(n)=O(n$^{3}$)
Hence as per definition,
f(n)<=c*n$^{2}$, f(n) can be n$^{2}$, n$^{2}$/logn, nlogn,n,constant,1/n,1/n$^{2}$,1/2$^{n}$,...
Similarly,
g(n)<=c*n$^{3}$, f(n) can be n$^{3}$, n$^{2}$, nlogn,n,constant,1/n,1/n$^{2}$,1/2$^{n}$,...
Solution:
[I] f(n)*g(n) <= [constant *largest possibile eqn in f(n) ]*[constant *largest possibile eqn in g(n) ]=constant*n$^{2}$*constant*n$^{3}$
i.e. f(n)*g(n)<=c*n$^{5}$,
Hence f(n)*g(n)=O(n$^{5}$).
[II] f(n)/g(n) <= [constant *largest possibile eqn in f(n) ] / [constant *smallest eqn in g(n) ]
Since the lowest equation is not bounded for g(n), it can be 1/n, 1/n!,1/2$^{n}$,1/n$^{n}$, and even lower than that
Hence f(n)/g(n) does not have an upper bound.