Answer:
[tex]\displaystyle E=e^{5x}[/tex]
Step-by-step explanation:
Exponentials
Properties of exponentials:
[tex]x^ax^b=x^{a+b}[/tex]
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Simplify:
[tex]\displaystyle E=\frac{e^{-2}\cdot e^{2x+3}}{e^{1-3x}}[/tex]
Multiplying in the numerator:
[tex]\displaystyle E=\frac{e^{-2+2x+3}}{e^{1-3x}}=\frac{e^{+2x+1}}{e^{1-3x}}[/tex]
Applying the quotient:
[tex]\displaystyle E=e^{2x+1-(1-3x)}[/tex]
Operating:
[tex]\displaystyle E=e^{2x+1-1+3x}[/tex]
Simplifying:
[tex]\boxed{\displaystyle E=e^{5x}}[/tex]
