Answer
$${e^{x\ln 3}},{e^{\pi \ln x}},{e^{\left( {\sin x} \right)\left( {\ln x} \right)}}$$
Work Step by Step
$$\eqalign{
& {\text{We have: }}{3^x},{\text{ }}{x^\pi },{\text{ and }}{x^{\sin x}} \cr
& {\text{Use the identity }}{y^p} = {e^{p\ln y}},\,{\text{then}} \cr
& {\text{ }}\underbrace {{3^x}}_{y = 3,{\text{ }}p = x}{\text{ }} \Rightarrow {\text{ }}{3^x} = {e^{x\ln 3}} \cr
& {\text{ }}\underbrace {{x^\pi }}_{y = x,{\text{ }}p = \pi }{\text{ }} \Rightarrow {\text{ }}{x^\pi } = {e^{\pi \ln x}} \cr
& {\text{ }}\underbrace {{x^{\sin x}}}_{y = x,{\text{ }}p = \sin x} \Rightarrow {\text{ }}{x^{\sin x}} = {e^{\left( {\sin x} \right)\left( {\ln x} \right)}} \cr} $$
