Comparing the value of $(1^r + 2^r +3^r +\ ...\ + n^r)^n$ with $(n^n)(n!)^r$, ${(n)^2n}{(n!)^r}$, ${(n)^n}{(n!)^2r}$, ${(n)^n}{(n!)^2r}$

Question

What will be my approach toward this type of question:

The value of $$(1^r + 2^r +3^r +\ ...\ + n^r)^n$$ where $n$ is a real number, is

A.greater then or equal to $(n^n)(n!)^r$

B.less than or equal to ${(n)^2n}{(n!)^r}$

C. less than ${(n)^n}{(n!)^2r}$

D.greater than $(n^n)(n!)^r$