If $w$ is a positive integer and $w^{3}=9 w$, then $w^{5}$ is equal to
(A) 59049
(B) 243
(C) 1024
(D) 3125
(E) 32
Since $w$ is a positive integer, then $w \neq 0$, so $w^{3}=9 w$ implies $w^{2}=9$ (we can divide by $w$ since it is non-zero).

Since $w^{2}=9$, then $w=3$ (because we know $w>0$ ).

Thus, $w^{5}=3^{5}=243$.

Answer: (B)