6．（2020•咸阳三模）若数列$\{a_{n}\}$为等差数列，$\{b_{n}\}$为等比数列，且满足：$a_{1}+a_{2020}=27$，$b_{1}\centerdot b_{2020}=2$，函数$f(x)$满足$f(x+2)=-f(x)$且$f(x)=e^{x}$，$x\in [0$，$2]$，则$f(\frac{{a_{1010}}+{a_{1011}}}{1+{b_{1010}}{b_{1011}}})=($　　$)$