For m, n ∈ I⁺, $\underset{x→0}{\lim}\frac{\sin x^n}{(\sin x)^m}$ is equal to

0, if n > m

Writing the given expression in the form

$(\frac{\sin x^n}{x^n})(\frac{x^n}{x^m})(\frac{x}{\sin x})^m$and noting that the $\underset{θ→0}{\lim}\frac{\sin θ}{θ}= 1$, we see that the required limit equals to 1 if n = m, and 0 if n>m.

Hence (B) is correct answer.