Answer:
[tex]1. ~e^5\\2. ~e^{\frac{3}{2}}\\3. ~e^6\\4.~ e^7[/tex]
Step-by-step explanation:
We have to simplify the given exponential expressions
Exponential properties:
[tex]e^0 =1\\e^a.e^b = e^{a+b}\\\\\displaystyle\frac{e^a}{e^b} = e^{a-b}\\\\(e^a)^b = e^{ab\\\\e^{-a} = \frac{1}{e^a}[/tex]
Simplification takes place in the following manner:
1)
[tex](e^2)^\frac{5}{2}\\\text{Applying the exponential property}\\\\=e^{2\times \frac{5}{2}}\\= e^5[/tex]
2)
[tex](e^2)(e^{\frac{1}{2}})\\\text{Using the exponential propert}\\\\= e^{2 + \frac{1}{2}} = e^{\frac{3}{2}}[/tex]
3)
[tex](e^{-2})^{-3}\\= e^{-2\times -3}\\=e^6[/tex]
4)
[tex]\displaystyle\frac{e^5}{e^{-2}}\\\\\text{Using exponential properties}\\\\= e^{5-(-2)} = e^7[/tex]
