Exercice 3

a) $\mathrm{e}^{3x}\times\mathrm{e}^{-2}=\boxed{\mathrm{e}^{3x-2}}$ ($a=3$, $b=-2$)

b) $\left(\mathrm{e}^{x-1}\right)^{4}=\boxed{\mathrm{e}^{4x-4}}$ ($a=4$, $b=-4$)

c) $\dfrac{\mathrm{e}^{2x}}{\mathrm{e}^{5-x}}=\mathrm{e}^{2x-(5-x)}=\boxed{\mathrm{e}^{3x-5}}$ ($a=3$, $b=-5$)

d) $\mathrm{e}^{-x+2}\times\mathrm{e}^{3x}=\boxed{\mathrm{e}^{2x+2}}$ ($a=2$, $b=2$)

e) $\dfrac{1}{\mathrm{e}^{4x-1}}=\boxed{\mathrm{e}^{-4x+1}}$ ($a=-4$, $b=1$)

f) $\dfrac{\mathrm{e}^{x+2}}{\mathrm{e}^{2x-2}}=\mathrm{e}^{(x+2)-(2x-2)}=\boxed{\mathrm{e}^{-x+4}}$ ($a=-1$, $b=4$)