Answer: [tex]e^{6}[/tex] .
Step-by-step explanation:
According to the division property of exponents : [tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]
For example : [tex]\dfrac{4^{5}}{4^{2}}=4^{5-2}=4^3[/tex]
Let's take one more example , [tex]\dfrac{5^{2}}{5^{3}}=5^{2-3}=5^{-1}=\dfrac{1}{5}[/tex]
The given expression : [tex]\dfrac{e^2}{e^{-4}}[/tex]
By division property of exponents , this will become
[tex]\dfrac{e^2}{e^{-4}}=e^{2-(-4)}[/tex]
[tex]=e^{2+4}=e^{6}[/tex] [Since (-)(-)=(+)]
Therefore , the required simplified expression would be [tex]e^{6}[/tex] .
