Question: User: sin^2(x)tan^(x)
1. The problem is to understand and simplify the expression $\sin^2(x) \tan^x$.
2. First, clarify the notation: $\sin^2(x)$ means $(\sin(x))^2$, the square of sine of $x$.
3. The term $\tan^x$ is ambiguous; it could mean $\tan(x)$ raised to the power $x$, i.e., $(\tan(x))^x$.
4. So the expression is $(\sin(x))^2 \cdot (\tan(x))^x$.
5. Recall that $\tan(x) = \frac{\sin(x)}{\cos(x)}$.
6. Substitute $\tan(x)$:
$$
(\sin(x))^2 \cdot \left(\frac{\sin(x)}{\cos(x)}\right)^x = (\sin(x))^2 \cdot \frac{(\sin(x))^x}{(\cos(x))^x} = \frac{(\sin(x))^{2+x}}{(\cos(x))^x}
$$
7. The simplified form is:
$$
\frac{(\sin(x))^{2+x}}{(\cos(x))^x}
$$
This is the simplified expression combining the powers of sine and cosine.
Final answer: $\frac{(\sin(x))^{2+x}}{(\cos(x))^x}$