evaluate e²ln(4). write your answer as an integer or fraction in simplest form.

Explanation:

Step1: Use logarithmic - exponential property

Recall the property $a^{\log_a(b)}=b$ and $e^{\ln(x)} = x$. Here, for the expression $e^{2\ln(4)}$, first use the power - rule of logarithms $\ln(x^n)=n\ln(x)$. So, $2\ln(4)=\ln(4^2)=\ln(16)$.

Step2: Simplify the exponential - logarithmic expression

Since $e^{\ln(x)} = x$, when $x = 16$, we have $e^{2\ln(4)}=e^{\ln(16)} = 16$.

Answer:

16