1. We need to determine whether the function $f(x) = \sin^9 x \cos^5 x$ is even, odd, or neither. 2. Recall the definitions: - An even function satisfies $f(-x) = f(x)$. - An odd function satisfies $f(-x) = -f(x)$. 3. Calculate $f(-x)$: $$f(-x) = \sin^9(-x) \cos^5(-x)$$ Since $\sin(-x) = -\sin x$ and $\cos(-x) = \cos x$, we get: $$f(-x) = (-\sin x)^9 (\cos x)^5 = (-1)^9 (\sin^9 x) \cos^5 x = -\sin^9 x \cos^5 x$$ 4. Compare $f(-x)$ with $f(x)$: $$f(-x) = -\sin^9 x \cos^5 x = -f(x)$$ 5. Since $f(-x) = -f(x)$, $f(x)$ is an odd function. Final answer: $\boxed{\text{odd function}}$