Find the limit as x approaches zero

Question

$$\sin(x)^{200}\over x^{199}\sin(4x)$$ as x approaches zero. I applied three times l'Hopital rule but i do not know if it is right. Any help appreciate. $$200(199(198(\sin^{197}(x)\cos^{3}(x)-\sin^{198}(x)\sin(2x))-200\sin^{199}(x)\cos(x))\over -64x^{199}\cos(4x)-9552x^{198}\sin(4x)+472824x^{197}\cos(4x)+7762164x^{196}\sin(4x)$$ And if it is right what next?Again l'Hopital rule?

Answer 1

$$\frac{\sin^{200}(x)}{x^{199}\sin4x}=\frac{(\sin x)^{200}}{x^{200}}\cdot\frac{4x}{\sin4x}\cdot\frac14\xrightarrow[x\to0]{}1\cdot1\cdot\frac14$$