Simplifier les expressions suivantes :

\[ \begin{array}{lll} a_1 = e^{\ln 13} \qquad \qquad & a_2 = e^{4 \ln 5}\qquad\qquad & a_3 = e^{-\ln 7} \\ \\ b_1 = e^{\frac{1}{3} \ln 27} & b_2 = e^{-\frac{1}{2} \ln 4} & b_3 = e^{\ln 3 - \ln 5} \\ \\ c_1 = \frac{e^{\ln 216}}{e^{3 \ln 6}} & c_2 = \frac{e^{8 + \ln 7}}{e^{9 + \ln 14}} & c_3 = -e^{-\ln \frac{1}{3}} \end{array} \]