Expressions composées - Exemples

On écrit les expressions suivantes à l'aide d'une unique exponentielle.

\(A=\dfrac{\text e^9 \times \text e^7}{\text e^2 \times \text e^3} = \dfrac{\text e^{9+7}}{\text e^{2+3}} = \dfrac{\text e^{16}}{\text e^{5}} = \text e^{16 - 5}= \text e^{11}\)

 
\(B=\dfrac{\text e^{-12} \times \text e^{0,5}} {\text e \times \text e^4 \times \text e^{2,75}} = \dfrac{\text e^{-12 +0,5}} {\text e^{1+4+2,75}}= \dfrac{\text e^{-11,5}} {\text e^{7,75}}= {\text e^{-11,5-7,75}} = e^{-19,25}\)    

\(C=\dfrac{(\text e^{5})^4 \times \text e^6} {(\text e^{3})^{-2}} = \dfrac{\text e^{5 \times 4} \times \text e^6} {\text e^{3\times(-2)}} = \dfrac{\text e^{20} \times \text e^6} {\text e^{-6}}= \dfrac{\text e^{20+6}} {\text e^{-6}}= \dfrac{\text e^{26}} {\text e^{-6}}= \text e^{26+6}= \text e^{32}\)  

Soit \(x,y\) deux réels,

\(D=\dfrac{(\text e^{2x})^2 \times (\text e^y)^4} {(\text e^{-x})^{-3} \times (\text e^{4y}) ^2} = {\text e^{4x - 3 x} \times \text e^{4y - 8y}}= {\text e^{x} \times \text e^{-4y}} = \text e^{x+(-4y)} = \text e^{x-4y}\)